2 party check

In march, I was hit by a 4 wheeler that ran a flashing red light. I wasn't going too fast, so she survived, and my damage wasn't so bad that I needed a tow. (Her car was totaled)
I filed a physical damage claim.
Now, the way my lp works, is I pay 15 cpm into a maintenance program that covers all repairs . I've paid in well over 30k in 2 yrs, and have not used even half of that. (Program, not account, I don't get it back If I quit)
I pay the insurance cost and truck payment.
My claim check is 2 party . ( happened in Michigan, and we are a "no fault" state)
My name is listed first, and it was mailed to my house.
The second spot is the leasing company name.
My truck is already repaired, (ie maintenance program)
I was told the only reason the leasing company name is listed is to protect their interest because they still own the truck.
Do you think there will be a fight over who's money that is? If the company tries to claim it's theirs, wouldn't that be double dipping?

 

It says "and"
Repairs are already complete.
The check is based on the actual invoices from said repairs.
I just don't want to "pay twice" for the same thing.
What I did, was mailed it to the lease company, certified mail, (without signing it) with a note asking for a signature and a business card , and a SASE to mail it back to me.
I figure, they can't cash it without my signature and I can't without theirs.
Sure, I could have just had anyone sign line 2 and did an online deposit, but that seems too easy and would backfire.

 

That 15cpm will cover all repairs and in the event of an accident, if I am not at fault , all repairs will be covered by the company, (if at fault , I'm responsible for the expense)
It doesn't specifically say anything about "although repairs have already been paid for in advance with 15cpm, we get all insurance settlements and claims with our name mentioned on the check"

 

Yes they would have as part of the warranty.
The company is the one who suggested I file a physical damage claim