Should I run this through my car insurance company?

During a recent vacation I backed into a boulder and put minor scrapes on the bumper cover of a rental car. Of course the company is being extravagant, and instead of just fixing the scratches, they state they need to replace the entire bumper cover. This is going to cost me a total of 700.00. My deductible is 250.00.

I did not get the collision insurance and I didn’t pay with a card that covers it.

Should I just pay for it out of pocket, or run it through my insurance? In the long-term, will the cost of my insurance premiums going up, be more than the 700.00 I’ll pay – as well as the blight on my insurance history?