There’ a saying is that no good deed goes unpunished.
Your generous offer of settling for only one week’s payment might hurt you if you choose to seek dispute resolution because now Airbnb can say that only the one week of reimbursement is subject to dispute, the idea being that you agreed to that.
A dispute resolution would likely require you to pay arbitration fees. These might be capped now but not for long as the new changes to the terms of service did not include a provision capping arbitration fees at $200. See. About the updates to our Terms - Airbnb Help Center
So you need to decide whether to bring a case against Airbnb. Your first step would be a letter (‘the 30-day letter’) advising Airbnb of the claim and your intention to arbitrate. This costs you nothing. If you’re serious you should do this ASAP. See 23.3: " You must send your notice of dispute to Airbnb by mailing it to Airbnb’s agent for service: CSC Lawyers Incorporating Service, 2710 Gateway Oaks Drive, Suite 150N, Sacramento, California 95833 ."
Time is of the essence as the new terms of service kick in sometime after March 30.2023 unless you decide not to agree to them, which will ultimately result in the cancelling of your account.
I don’t know if the new arbitration payment rules will apply to you. Your claim arises under the current terms of service but its resolution will likely occur under the new terms of service.
If the new arbitration rules (i.e., no $200 cap on fees you pay) apply to you, you might well choose not to risk paying it to seek your claim resolution with an arbitrator (I wouldn’t in your situation because I’d be concerned that your offer to settle for one week might be an offer that Airbnb will say it relied on and to which they might argue you revoked too late (i.e., after they refunded the guest).
Your rebuttal, I suppose, is that Airbnb’s refusal to pay you the one week’s stay was a refusal of your offer, the non-payment to you further shows Airbnb did not accept your offer and that in fact nothing was paid to you and so the original terms and conditions of the reservation applies. I don’t know what the stronger argument is, whether reasonable arbitrators might disagree on your remedy.
Your first step (and it’s free) – and time is ticking – is to send that 30 day letter advising Airbnb of the dispute and your hoped-for remedy.
If Airbnb goes ahead in arbitration it will need to pay substantial arbitration fees also ( $1,700 is your filing fee, plus arbitrator compensation, $750 for a desk arbitration unless you can successfully argue that the old./current $200 arbitration fee cap should apply since the incident arose before 3/30/23 and therefore indisputably under the old Terms of Service).
→ So you might take that first step by sending that letter and seeing how Airbnb responds.
If Airbnb calls your [bluff?] by seeking arbitration, I’d probably pass (unless your fee is capped at $200) as I don’t know whether you’ll win.
But Airbnb might just pay you the money (seems unlikely to me), or offer you pennies on the dollar (they can calculate an offer that would be uneconomic to refuse because you need to pay the arbitration costs, say in the $2,500 ballpark,) to go through with the arbitration, say they’re willing to arbitrate, OR they could have you file your claim in small claims court.
If you end up going the small claims court method (check what the limit for which you can sue is in your jurisdiction, often a number like $10,000) you will have minimum costs to proceed. This might be your best bet but Airbnb needs to tell you to go down this route, that it is foregoing arbitration, before you can do so.
Since this is a long-term stay my understanding is that the cancelling guest here would need to pay for 30 nights. So that’s what you’ll argue is at stake.
Airbnb will likely argue that the one week of rental payments that you admitted you offered to accept and which Airbnb awarded is the amount in dispute.
→ It would be helpful to you to get Airbnb to explain on what basis it cancelled the reservation without penalty. You don’t want to be surprised with their answer later. Asking them might surface that they have no explanation under their policies (unless they do).
They can just ignore you, stop responding to you. How will they wiggle out of it? Easily.
There’ a saying is that no good deed goes unpunished.