Reset it, and note that the counter will now be off by 7000 miles. Do a quick search and you can figure out roughly when the next services are due, since the counter will be incorrect for these particular items. Make sure (as per the above link) that the items it's calling out were actually done in the 'full service'. Somehow, full service means different things to different people.
You said they did "full service." Did that include transmission fluid ("3") and the VTM-4 (rear differential) fluid ("6")? Did it include rotating tires ("1")?
The "3" and "6" codes sound about right for your current mileage.
The oil change ("A") would be a marginal thing, but the MM system uses sensors to gauge somewhat how severely you have been using the vehicle. So that might also be a good idea.
If you brought your vehicle in because you had reached 30,000 miles, and the MM wasn't calling for any service at the time, it's also possible that they overlooked resetting it because there was no visible indicator. (Others may agree with me that they SHOULD have reset it anyway.)
Look at the order for your last service and see what they actually did at 30,000 miles. If they did AT fluid and VTM-4 fluids, you don't need those again. If they didn't, you ignore the VTM-4 fluid at your peril--it takes a beating and breaks down around the mileage you have. Even more if you're towing, where they recommend a change every 15,000 miles.
Frankly, there is nothing to reset at 30k miles that would affect the tranny callout at the OCI prior to reaching 45k miles. So the dealer may well have reset the MM clearing all codes as expected. I would not reset the MM yet until you know for sure what has been done. I suspect it was properly done for whatever service was performed at 30k miles. What was the callout then? Do you remember?
Here is why I think you're getting the A136 code at 37k miles. The MM system will call for maintenance at the OCI prior to reaching the next mileage limit. For instance, on the old normal service maintenance schedule, the first tranny fluid change is at 45k miles. If you just got the 15% alert at 37k miles, the MM system thinks that you may exceed 45k miles before the next service is due, so it calls out for the -3 service at the OCI prior to reaching 45k miles. You may well have over 38k miles before reaching 0% on the MM and having the service performed. Add the MM projected miles until the next OCI and you may exceed 45k miles.
Full service at 30k miles does not remotely begin to describe the maintenance performed. There is no 30k mile maintenance interval from Honda. There may well be a 30k mile maintenance interval from the dealer. But remember, the dealer is simply a franchise and is not Honda, per se. They are merely permitted to sell and maintain the vehicles, but are free (AFAIK) to maintain them at or more often than Honda recommends. The latter is normally the case as it brings in more $$ for the shop.
Over maintaining is not a bad thing, but your wallet may object.
Now if the shop did the rear diff (-6) service and the tranny fluid (-3) service at 30k, they really don't need to be done again at 37k miles. In that case, I would make sure that all of the appropriate service was done (transfer assembly fluid changed too), and if so, I would reset the MM when the oil and filter change is performed and ignore the callouts for the items recently done.
But you will have to note that you are now outside the MM parameters and make a note of when to do the next tranny fluid/TA/rear diff service. Your MM callouts will be out of sync with your new maintenance schedule.
Whereas the MM would likely call out the -3 service at the OCI just prior to reaching 45k miles, then again 30k miles later prior to reaching 75k miles, you may now be on a 30/60/90k mile interval for those services since the first change was performed early at 30k miles instead of 45k miles. The MM system is not smart enough to know when service is performed early or off schedule.
The MM callouts are grouped around OCI (oil change intervals). There is an A and a B main code and also related numeric subcodes (1 through 6). Honda tends to group maintenance around an OCI for the sake of convenience.
When you reset the MM, the system expects that all maintenance called for has been completed. It will not call for maintenance on those specific systems again until the next time they are due. So if you don't complete everything on the callout at one time, make sure to note the remaining items and do them when possible. That will keep the MM in sync with what needs to be done.
The MM will callout out specific items at the OCI just prior to reaching the miles they are due. For instance, on a new vehicle, the rear diff (VTM-4 unit) should have the VTM-4 fluid changed by 15k miles. If you are getting 6500 miles OCIs (like I do), then you should expect the -6 callout when you get the MM alert (B16 likely) due at 13k miles.
I find the alert pops up at 15% oil life remaining. For me, that's about 1000 miles of driving until it hits 0% (which is when I do my maintenance). Yeah, I run over a few hundred miles from time to time. No big deal.
But the point of this is understanding how the MM works and what to expect when you get the callouts.
Here's a copy of a normal service maintenance schedule. I find it to be a bit more conservative than the MM callouts in a few areas and a little less conservative in other areas.
For instance, the OCI is 7500 miles (but your MM is likely less than that... a notable exception to being more conservative than the MM); rear diff fluid at 15k, 30k, then every 30k (MM is 15k, then every 30k in my experience), tranny at 45k, then every 30k (along with the TA). OCI callouts on the MM system can vary widely, depending on operating conditions... 3k - 10k or so, I don't really know the design parameters, but I know some here get 10k OCIs.
It's really a pretty good schedule for normal service.
When you choose to maintain your vehicle on a different schedule than the MM system suggests, you need to be able to keep up with the schedule manually.
Edit: and as Matt noted above, the maintenance interval is roughly halved if you are in severe service operations. (frequent towing, etc.)
As was said, the MM callout for the tranny service wouldn't have happened at 30k miles. the "6" callout should have happened at or before 15k and 30k miles. The MM monitors your driving and estimates the usable life of the fluids based on an algorithm. It will call out certain things in advance. My "4" (timing belt) indicator came on at 101k miles because the service was going to be due before the end of the next oil change interval. The only thing I actually use the MM for now is engine oil. I drive very little these days (less than 6000 miles per year), so I change my tranny fluid, transfer case gear lube, VTM-4 fluid and other fluids much more often than what the MM would call for in mileage. If I went by the service schedule, I'd only be changing many of the fluids every five years - that's a no-no in my book.
Just as a note, there is no "30,000 mile", 60,000 mile", etc. service that is called for by Honda. It's something that is made up by the dealership service people to get you to do a bunch of services all at once. Most can be pretty expensive for simple fluid changes. Don't let them fool you. If you drive a normal amount of miles per year and don't drive like a crazy person, follow your MM.