The term المقاصة has several different meanings, depending on context, mostly related to financial obligations:

1. In the context of personal debts, if you owe me $40 for cutting my hair, but I already owe you $30 for mowing my lawn, then you only have to pay me $10.

2. In the context of banks, when you pay me for cutting your hair, you write me a check, which I deposit in my bank. But your check is drawn on another bank, because your bank is not my bank. So my bank must draw the money from your bank. But your bank also has many checks that are drawn on my bank. This happens everyday, and it involves all banks against all other banks. So a process of financial arithmetic is performed to determine which bank pays how much to which bank.

3. In the context of lawsuits, when you file a lawsuit, you can win or lose. If you lose, the judge, in some jurisdictions, may force you to pay the fees of your opponent's attorneys. It is not clear why this is called مقاصاة in Arab countries, but it is. Technical terminology, especially in some fields, is sometimes quite arbitrary. It does not matter, so long as we all know what it means.

Clearly, your context falls under the third meaning of مقاصاة, which is quite different from the first two meanings explained above. In this kind of context, we simply say that the court has ruled that one party PAYS the fees of the attorney of the other party. There is no special terminology for that.