I'm licensed for chemically treating trees, so hopefully I can give a decent answer to this question. First of all there are not many chemical treatments that are going to be done to an apple tree, especially not one that is in a home owners yard. Orchard work is something different entirely, but I do not beleive that is the case in this situation. the most common pest in apples is a coddling moth. Coddling moths are treated using pheromone based glue traps set out in the early part of the year and with these traps there is zero pesticide exposure to the tree. there are other reasons why a chemical could have been applied, but I can not think of anything that would pose a threat after even a year, let alone 6 years. Most foliar sprays (sprayed on the leaves) only last about 3-7 days when sprayed on an organic surface unless that spray has some sort of systemic action. I can only think of one systemic chemical, imidacloprid which is used in vast amounts on a variety of trees for a variety of insects. This comes in many forms, and I believe apples are not on the label, but that doesn't stop people from using it. Anyhow even when used as a system drench it only stays in the tree for up to one year. Actually it starts wearing off after a few months but may have a residual effect for some time even after it starts to wear off. If it were me, knowing what I know, I would give the clippings to my chinchillas. I really doubt you have anything to worry about.