[Landlord US-MA] Unhappy tenant

Recently purchased a house with an existing tenant. The house needed repairs - new roof, foundation repair, mold, plumbing, etc. It's costing 100k. The tenant was aware of all the work that was about to be done but has since complained every step of the way, slowing the entire process—late-night texts complaining about the noise of the repairs that day, etc. We have considered the tenant's needs all the time, rescheduling contractors, ensuring air quality is fine, etc., and notifying them of what the loudest days will be. But still more complaints. They've asked for compensation because of the noise, they've subtly threatened they're going to sue.....for noise.
I'm debating whether to give them money, however, nothing illegal has been done, and I fear it would encourage the tenant to walk all over me. Thoughts, should I?