What should I do about this request?

I'm sure my answer is too late as well but I know this happens sometimes that you get these last minute requests with little to know info. Any time I've had what I would consider "hinky" like that, especially last minute, I would require the answers to my questions over text or phone call, and even ask more than I normally would. I haven't ever met with anyone I wasn't comfortable with; if after they didn't respond to the questions or the answers weren't clear, I politely decline the request. If someone really needs care for the dog(s) they will take the time to answer your questions and send photos of their dogs, or update the profile for you to see. I hope that it all worked out!

Strange that your question from almost two days ago just showed up, so this answer may be too late.

Yes, many people do not fill out enough information to decide if the job is right. Definitely use the messaging system online r the app or the rover generated phone number to gather more information to help you decide. Ask all questions that are important to you. It's highly recommended to have a meet& greet (where you get to know the dog and exchange more information) prior to booking a service,

I have had these types of requests and declined them.

I have had requests without meet and greets due to circumstances and they have worked out, but I wouldn't make a habit of it. Example: I live in a college city and some people from out of town were stopping for the weekend to go to a sporting event, so we couldn't do a meet and greet. I got a lot of answers from them before hand and asked the right questions, but I also had a backup plan if our dogs didnt get along.

Only time and experience will tell you what you should or should not book, but I can say it sounds like you are uncomfortable and shouldn't ever book if you feel uncomfortable.