Here's how I would handle this situation.

Say I gave my Border Collie Molly a treat. If I wanted to go take it, and she growled at my hand as I was reaching, I would sternly say "NO!" and take the treat away and she lose her treat for a while.

When going to give the treat back, I would make her sit.

Everytime I give her a treat, (and if she growls) I would repeat this.

It does sound like your dog is toy/treat possessive. I would do some researching on it. As another member said, the NILIF program is excellent.