the dealer did buy the part for me.
Good. That gives you some leverage. Not a lot, but some. First, here are the specifics on the warranty coverage; I'll follow that with my suggestion on how to proceed.
Comptech has a contract with Acura through which Comptech parts can be ordered from, and installed by, any Acura dealer. People mistakenly think that this means that the car still carries a full Acura warranty even after installing the Comptech parts, but this is not true. The warranty coverage is the same with Comptech parts as for parts from any other aftermarket vendor: Warranty coverage on the Comptech parts are covered by Comptech, and the Acura warranty excludes any damage caused by the installation and use of the Comptech parts. Although I don't know if it is explicitly stated anywhere, any damage caused by improper installation would be the liability of the installer (the dealership); most dealers would make good on any such damage, but only (and this is a BIG stipulation) if it is clear that their improper installation caused the problem. "There lies the rub", as they say. Right now you have a situation where Comptech and the dealer are pointing fingers at each other, each claiming that the other is responsible; neither wants to get stuck with the bill, and no one is budging. I assume you're dealing with Shad at Comptech and with your dealership's service manager. (If not, then try to work through those two individuals first.)
First, you ought to think about what your objectives are in resolving this dispute. Obviously, you don't think you should pay for the repair - regardless of whether the problem was caused by the part or by the installation. Or, if you have to pay SOMETHING, you want to pay as little as possible. But also, more specifically: Do you want to get another aftermarket R&P installed? Do you want to get your stock R&P put back in the car (assuming you still have it)?
I would suggest you try using Acura (corporate) as a go-between to resolve the dispute. Acura has a National Service Manager. Reporting to him/her are six Zone Service Managers (ZSM), one for each of the six zones in the United States. Reporting to each ZSM are a bunch of District Service Managers (DSM), each of whom covers maybe a dozen dealerships in one or more cities. The DSM's call on the dealerships and make decisions regarding Acura warranty coverage when there is a customer dispute at a dealership. These are reviewable by, and appealable to, the ZSM.
I would call Acura Customer Service at Acura HQ in Torrance (the toll-free number is in your owner's manual), explain the situation to them, and tell them that you'd like to discuss it with the Zone Service Manager for your part of the country. See if they will put you in touch with him/her. If they only put you in contact with the DSM, that's okay, try working through the DSM (knowing that you can appeal to the ZSM if you can't get it worked out).
Once you reach the ZSM or DSM, just explain the situation, calmly and respectfully. Tell him that you're not happy being without your car (you can't use the phrase "customer satisfaction" too often). Don't tell him how to resolve it - IOW, don't tell him you think Comptech, or the dealer, or Acura, should pay for the repair. Just tell him that you had a part ordered by, and installed by, your local Acura dealer, from their vendor. It failed. Tell him how you would like it resolved - whether you would like another R&P installed, or your original stock one. Concentrate on the fact that you don't think you should pay to make that right. The ZSM/DSM should be sympathetic. Then leave it up to him to work with Comptech and/or the dealer to get the repair covered. Let him come back to you with a resolution. Hopefully he will get one or the other to step up to making it right; he may or may not ask you to pay for a portion of the repair (perhaps half the labor) but hopefully not most of it. He may call it "goodwill" (as a way of paying for part or all of it without admitting any responsibility for doing so), and that's fine. If he isn't able to offer any coverage for the repair, then you can ask whether it could be split somehow between those concerned. Keep in mind that paying part of it is still better than paying all of it, and this may be the best you can do by working directly with these involved parties.
If you are still not able to reach a satisfactory resolution by going this route, then you may need to take further steps. These might consist of appealing to your local Better Business Bureau (many such offices offer free arbitration services to resolve such disputes without accumulating legal costs to do so), and/or using the legal system, either on your own (most civil jurisdictions have a "pro se" court, commonly known as "small claims", for settling disputes below a specified dollar threshold) or with the assistance (and cost) of an attorney.
Good luck.
By the way what mods have you done to your car???
Just the brakes (pads, rotors, cooling ducts), using the original calipers.