No lawsuits, no drama this time.....
Let us know the outcome, and yes, me the way I am, I would offer some money just to settle everything.
Legally once a property is closed, the buyer has accepted it and the Seller no longer has any legal responsibility. I can easily imagine the Seller simply saying, "You asked for a credit and we gave it to you, sorry the termite company made a typo, you need to speak with them" Ethically this isn't the right thing to do.
There's a number of things that I feel need to be considered. One you as the buyer's agent should have assumed responsibility for the termite inspection, this was to the benefit of your client and the seller should not have been involved at all. You probably should also have questioned an estimate of $280 which strikes me as ridiculously low unless they were only going to spot treat a small area.
Now the fact is the Termite company did supply a written proposal and you may want to review the language on it carefully. Many times the language of the "proposals" is actually that of a contract and it's possible you might get the Termite company to meet you somewhere in the middle as they should accept some responsibility for their typo.
It would be nice if the Sellers would contribute a little more and I'd certainly pressure the listing agent to pursue this and mention that there's always the possibility of the buyer filing a formal complaint against you and them with the real estate commission which would be a problem for both of you. You as their agent should also be prepared to make a contribution. I'd also suggest getting a couple of more estimates as based on what's transpired so far I wouldn't extend much trust to the termite company that prepared the quote.
I would suggest speaking with your BIC to see what their thoughts are. Were it me I would be prepared to do whatever was necessary to satisfy my buyer and would in the future would remember that it's my responsibility to order inspections and gather quotes for my clients and would not permit anyone else to do my job.
I hope things work out and that it doesn't end up costing you too much.
The buyer asked the seller to remediate the problem.
The seller got an estimate and the wrong estimate was presented to the buyer. The buyer accepted the resolution to the problem in the form of a credit in lieu of getting it treated.
If the both parties had known the actual amount involved, would they still come into an agreement?
The problem here is not who should be responsible but how to settle this AMICABLY outside of closing.