You need proof rather than supposition.

It is indeed illegal to feed deer in Illinois. That includes grains, salt/mineral licks, hay or whatever that is placed where deer are encouraged to partake. If feeding livestock and a deer eats it it is OK.

Have you overhunted or pressured the deer on your side of the fence? If they have no pressure on the neighbor's land, it is logical for them to congregate there.

Bust 'em if you have proof, otherwise leave them alone and work to make your land better than his.