Clearly we might infer that Myrtle's repeated absences from their home in the Valley of Ashes might have aroused George's curiosity, however, in Chapter Eight, after Myrtle has been killed in the hit and run, we see that what really made George suspect something was when he discovered the dog-leash that Tom has obviously bought for Myrtle for her dog in their appartment. Note how it is described:
There was nothing in it but asmall, expensive dog-leash, made of leather and braided silver. It was apparently new.
Clearly George knows that, firstly they could not afford such an item, and secondly there would be no need to buy something like this because they do not own a dog. It is this, of course combined with the way that Myrtle reacts when she sees Tom in Gatbsy's car, that makes George suspect that she is having an affair.