Odd Situation With House Sale My Realtor Says She Has Never Seen Before.

I am currently under contract to sell my house. The buyers went through inspections per usual and decided to have an HVAC guy look at our unit that has had zero issues. The buyer allowed the HVAC guy to make a repair on my unit without my presence, permission, or even knowledge. They are now saying they want to terminate unless we provide seller assist for things that do not need to be fixed, which I won’t agree to. I wouldn’t have cared about the HVAC work if they end up buying the house, but if they terminate I will have a problem since I only allow one specific person to work on my HVAC. I have no idea who they hired, and neither realtor was in the house. My question is- if they do terminate, do I have any legal standing to make them pay for my HVAC guy to come look at the system to see what was done during this unauthorized repair? Is it even legal to have work like this done on someone else’s house? I don’t know what she was thinking and not sure what to make of this. Thanks in advance!

Edit: the buyer paid for the repairs and has not asked to be reimbursed. My problem is that now that they are wanting to terminate, the most expensive piece of equipment in my house has been worked on by someone I would NOT have hired. My FIL is an HVAC man and I don’t ever go through anyone but him as I’ve come across some very shady characters in the business before.

Update: going through my sales agreement and it says “all inspections must be non-invasive, unless otherwise agreed in writing”. Also says “seller may retain all sums (earnest money) should buyer violate or fail to fulfill any terms of this agreement.”. Would the unauthorized repair be considered invasive in real estate/legal terms?