To claim or not to claim

I have a 2023 Kia,that needs to be repaired because of a damaged heat shield and front bumper. This is not the result of a collision or anything.

My deductible is $500. The quote that I got from the collision shop is for $2700.

I actually had to replace this heat shield already the first year I owned the car because I live in a colder climate and it is attached to the frame of the car with plastic claps, which, apparently in the cold weather can break very easily.

I'm in New York State. I have insurance through Geico and have been with them for 18 months with no claims. The last auto claim I had was an accident 6 years ago. I'm a man; mid 30s.

I would like to know if I do decide to put this through insurance will it make my rates go up enough that it won't be worth it in the long run? Currently I'm paying $137 a month for my auto insurance.