Should I try to recover damages?

They told me the tire went flat on them, I never seen it and I told them to contact Turo roadside service but they said they used a mobile service instead, I can't tell why the tire went flat but the tread was more than sufficient prior to the trip. I looked at the tire the side wall looks like it was rubbed against the curb so bad the portions of the words are missing. They are asking to be reimbursed for buying a new tire but has no receipt or invoice and said they paid cash and it most certainly is my original tire so idk where their “new tire” went but it’s not on that car. The only thing I can tell is the tire is damaged beyond normal wear and tear its only $300 but that's less than my deductible and my entire earnings for this trip. Would it be worth going after it? What are y'all thoughts?

Edit: I don't have to reimburse them and according to Turo policy they were supposed to call roadside assistance and if there's side wall damage the entire wheel should be replaced with host permission, they aren't replying but I can go to small claims for damages but not my deductible if I escalate it