To narrow your answer down even further, think particularly about whose house this tree is located near. Is there a person near this location who would intentionally enjoy watching Jem and Scout find the little surprises and tokens that he/she leaves? If so, who would that be, and why?

Moreover, you may want to consider any "neighborhood rumors" that may have been mentioned about certain people who live near this tree -- who has been suspected of odd or objectionable behavior, and how might the giving of gifts contradict those rumors and presumptions? Once you find the answers to these questions, you'll know the secret of the tree's "gift giver."

You should think about where the tree is located and what "gifts" are found there. Someone seems to be leaving items specifically tailored for Jem and Scout. Who knows them well enough to do this? Also, and maybe more importantly, we give gifts not only to provide people with things they will enjoy, but to see their reactions, too. Perhaps whoever leaves the items in the knot-hole enjoys seeing Jem and Scout find them. Who has a great view of the tree?

This is really a question that you should answer yourself.  The reason I say that is because everyone who answers questions on here knows where the gum and pennies are coming from.  So it's hard for us to wonder where they're coming from.  From the sound of the question, I think your teacher is more interested in your thinking than in the actual answer -- who actually puts them there.

Jem and Scout seem to think that they belong to someone who rides the bus to school.  That person has stashed them and forgotten them.  This makes sense because who else would hide stuff like that in a tree?

I guess you might want to consider that question.  What kind of person would leave stuff in a tree other than a kid?  I suppose it would have to be someone a bit strange, right?   And think to yourself where the tree is.  Maybe between those, you can figure out who it is.