What happens if you keep using COBRA when you get a new job?

I took like 3 COVID tests in March/April, making sure to go to places that would be reimbursed by the city/county, because my insurance only covered like 3 places and there were never appointments. The city/county basically said “If your insurance doesn’t cover it, we’ll pay for it.” Works for me.

So then my insurance says “Oh, hey, we don’t cover these places, so this is how much they should charge.” But it seemed, as advertised, that the city/county paid for them, since I don’t think I ever received a bill from the test suppliers.

Yesterday, I got a letter from my insurance company, and it’s a check for like $130. The explanation: “We paid the member for this claim because the doctor/facility is not in the plan’s network. The member is responsible for paying the bill they receive from the doctor/facility.” and also “Going to this lab uses out-of-network benefits — if your plan has them.” And then also Claim number, received date, and “Lab: PAY TO MEMBER (Not in your plan)”

So I’m guessing they thought I forked over the money to the lab on the spot, and now they have some out-of-network COVID benefit thinger that I wasn’t aware of and they’re trying to reimburse me.

So, um… do I just cash the check? Do I… try to figure out which government entity actually got the bill for these, and write them a check? What’s the way forward here?