There's a loaded question if ever I saw one.
What we don't have to ponder is; did you take the boat back and try it and like it or not like it? I mean, results can be everything. If, indeed the engine was "carboned" up, what was done to "de-carbon" it?
I really don't think it should be too carboned up even if you had idled it for most of the 110 hours so I would question them as to how they determined that fact. Such as, did they use a borescope to look inside the cylinders? Was the compression too high? Was a valve hung open because of it? Did the carbon bunny come out and talk to them? Don't give them ideas, just ask.
If they are the dealer that sold you the motor and hung it on the boat and got it ready, THEY are probably the party that "messed" with the base idle screw. So, why in the world would YOU have to pay for them putting it back where it belongs?
But, the bottom line is if you are now happy with the way the engine runs and the problem got solved, it might not be an unreasonable charge at all, depending on what exactly it was that they did. If they ran an upper engine cleaner through the intake to knock out the cobwebs and the problem went away, I would say two hours labor MIGHT be in order.
It really doesn't matter what we out here in cyber land think. It's YOU that has to be satisfied. And, if you are not, then you will need to go to bat for your convictions. If you think they are not being honest, you need to call them on it and, yes, take your business someplace else or, at least, get another opinion from a shop that has a VERY good reputation. Which, in the outboard world, can be fairly hard to do. Honda does have a system in place for a regional guy to take a look at your case if you feel ripped off by one of their dealers and getting them involved may be something to consider.