The easy way out is to just ask the repair facility to price match with a new OEM cover. They're likely to do it anyway without you mentioning it. I do NOT bid new OEM bumper covers if a reman is available. I believe the last time I bid a new OEM cover on an estimate was last fall.
And it really doesn't matter what you're policy covers, you're a claimant. You don't have a contract with Geico. They are going to warranty your repairs (if you use their repair facility). In fact, consider yourself lucky to have had them even bid a reman OEM over an aftermarket. Get hit by Geico here and you're likely to get some non-CAPA aftermarket crap bid.
If your policy will get you something better (highly unlikely), you'll have to file a claim on your own insurance, pay your collision deductible and have your carrier subrogate.
And don't worry about getting a recycled (used - from salvage yard) bumper cover. You'll NEVER get a front one because of rock chips, scrapes from parking blocks, etc. (unless you get a company that bids/negotiates cleanup) and rear covers are rare. Best case, I'll buy an NIQ assembly with a cover so bad a rebuilder wouldn't touch it for a fraction of the cost just to get the absorber, reinforcement bar, stays, supports and brackets and still buy a reman cover to finish it off.
Also, due to certain manufacturers repair procedures, most carriers are getting away from wording about repair to pre-loss condition. Some manufacturers have factory rivets that get drilled out and replacement parts are welded in, various sectioning procedures for pillars and frame rails will show signs of repairs, headlight tabs showing fracture lines after repair, etc.
And it really doesn't matter what you're policy covers, you're a claimant. You don't have a contract with Geico. They are going to warranty your repairs (if you use their repair facility). In fact, consider yourself lucky to have had them even bid a reman OEM over an aftermarket. Get hit by Geico here and you're likely to get some non-CAPA aftermarket crap bid.
If your policy will get you something better (highly unlikely), you'll have to file a claim on your own insurance, pay your collision deductible and have your carrier subrogate.
And don't worry about getting a recycled (used - from salvage yard) bumper cover. You'll NEVER get a front one because of rock chips, scrapes from parking blocks, etc. (unless you get a company that bids/negotiates cleanup) and rear covers are rare. Best case, I'll buy an NIQ assembly with a cover so bad a rebuilder wouldn't touch it for a fraction of the cost just to get the absorber, reinforcement bar, stays, supports and brackets and still buy a reman cover to finish it off.
Also, due to certain manufacturers repair procedures, most carriers are getting away from wording about repair to pre-loss condition. Some manufacturers have factory rivets that get drilled out and replacement parts are welded in, various sectioning procedures for pillars and frame rails will show signs of repairs, headlight tabs showing fracture lines after repair, etc.