Too much transmission fluid???

Yes it can. Too much fluid can cause foaming, introducing air into the hydraulic system. You should drain and refill it to the proper level. Check it on a level surface with the car running.

...and if this is beyond your confidence/competence level, and if the fluid is pretty & clean & not burned-smelling(i.e., relatively recently changed), you might use a small siphon hose & remove the excess thru the dip stick tube. s

First, it ain't two quarts over. No dipstick has markings for overage like that. You figured it was over that much by interpolating the segment on the dipstick that does have relevance. The dipstick is not linear. Once the level is at the full mark sometimes even a cupful extra will bring the level way up the stick. So perhaps you are 8-12oz. over. Still, it's worth bringing down to the full level. If you can't siphon some out you could pump some out using a tiny hand pump that goes on the top of an outboard motor gear fluid bottle, about $3 at my store.