@Jerry422 Since you are new to hosting, I hope you've looked carefully at the Host Guarantee. It explicitly states that Airbnb does not cover damage caused by pets. This is one of the many reasons why some multi-platform hosts allow pets on other listing sites but not through Airbnb. Another thing that is unlikely to protect you from damage is prayer - if God were an insurance plan, he'd have a 1 star rating on Trustpilot. You'll want to make sure your STR insurance covers this.
To answer your questions:
1. If you're going to send a resolution request, do it as soon as you've noticed the pet. There's no reason to wait until the end of the stay, as they no longer have any incentive to accept the charge rather than dispute it.
2. No absolutely don't do that. As long as the stay is in progress, the guests are your customers, and a "slap on the wrist" is not appropriate for that relationship. You're entitled to the fee, but it's best to approach it professionally rather than feign a wink and a nudge.
3. Ignoring it is a great way to advertise that you're a doormat who's easily manipulated by guests. Unfortunately, with a brand-new listing you're a magnet for the kind of people who are eager to exploit that. It might now be too late in the stay to be worth bringing up, but at the very least, be sure to state in your review that the guests brought a pet without informing you. No responsible pet owner would behave this way, and these are not desirable guests for future hosts.