Filing a claim with Chase (but not supplying any documents) preserves all of your rights for 365 days, takes 2 minutes and $0. Seems like a no-brainer if there's any question at all.
Just a random data point: I screwed up a bumper on a rental about 3 years ago (hit a high curb while parking). I thought the damage was pretty visible but (foolishly or not) I didn't mention it when I returned it. I did take a few pictures just so I could have some evidence of the extent of the damage if they tried to bill me for something more. But I never got a bill or anything. So sometimes bumper damage does get missed. The problem is you won't know definitively for months.