3 pieces might be the limit for not affecting the pitch or, in practical terms, not affecting it too much. I know when I need to use 4 or more, it really does affect the pitch.
Putting it in the back of the thumb hole should NOT and if you need more than 2 or 3 pieces, consider putting it in the back and then putting a piece of slick black tape over the white tape (assuming we're talking about the white thumb hole tape here). That way, the thumb hole will get tighter, you won't affect the pitch anymore than you have to, and the back of your thumb won't stick to the abrasive white tape.
And, of course, next time, get a smaller thumb insert or have the thumb hole made smaller, keeping in mind that the thumb hole must be as large as your thumb ever gets.