The traps work without chemicals. Chemicals are the issue

Contact the previous owner and ask them if they paid for the traps. If so, tell Massey where they can go. If, not, let them waste their labor to pick up something that is used and they will have to throw away.

You bought the property including anything on it. Legally they can make a claim to prior owner.

IMHO, smart money would NOT use a device that draws termites to the house in order to get rid of them. Just use chemical treatment, and get it from a company that will provide a damage bond on the house.

I agree. The chemical treatment is better. It is cheaper, requires no monitoring, and it won't interfere with potential future landscape changes.

Further clarification?
 

After reading the whole thread thus far, it seems apparent that the terms "trap" and "bait station" are being used as if they are the same thing. They are not. Traps catch bugs. When full, throw them out and replace. Bait stations hold bait for insects (typically ants) to take back to the nest to kill the whole colony. These are, most likely what the company would like to retrieve.