Whoops, just went to answer without reading past comments, so if I'm repeating please forgive me.
I'll look at the other responses after I type mine.
First, I would say yuck to the chewelry. Children especially in this age category are not well aware of how viruses spread. They often share things even when they are not supposed to. They pick their noses, put their hands in their pants, don't wash their hands then touch stuff. Ugh! The thought horrifies me and I am not, I repeat I am not a germaphobe, I just know. I've worked with a lot of children and witnessed it.
With that said, there is much research on how chewing strengthens the jaw, neck, and core--all connected according to my son's speech therapist. So she provided chewy tubes for him in preschool to use instead of putting toys in his mouth.
When I had my own classroom, I allowed the children to chew gum (gasp), because there is also research that the chewing helps with concentration. My rule in the class was they were allowed to have it as long as I didn't see it, they chewed with their lips closed, and if I ever found it anywhere on tables, rugs, etc. That would be the end of this priviledge. The children were to save their wrappers, and spit the gum into the wrapper or a piece of paper before they left the class to go to PE, recess or another classroom. I cleared this with my principal, and the other teachers knew what was going on.
Only twice did I ever find gum any where besides where it was supposed to be, and you should have seen the children scramble to clean it up regardless of whom it belonged to, because they didn't want to lose the privilege.
So I say, discuss some other options with the teacher to get the chewlery out.