Is there an expression meaning we don‘t owe each other any more？
“Now we are even” comes into my mind, but I think it is more of something to say after getting back at that person. I am looking for something to say after doing things for that person so I am no longer in his/her debt.

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If it’s a casual conversation. You could ask: 
Are we cool? OR We’re cool now, right?
Are we good? OR We’re good now, right?
Are we OK? OR We’re OK now, right?
If it is a more formal conversation You might ask: Have I fulfilled my obligation (to you)?
In all of these instances you are asking the other person if your debt / obligation to them has been settled.

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We can say:
-We're good.
-We're quits.

You can say,
-That should bring us back into balance
-That evens the odds (a bit)

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"we are quits" "we are all square" are better for your context in the UK.

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Thank you！Robin. By debt, I meant owing someone a favor.

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In the US if you say “we’re quits”, that could mean you are breaking up with someone. Saying “we are even” really depends on the context. What kind of debt are you talking about? If it’s monetary debt, there is nothing wrong with saying we are even. Clerks use this when a transaction has been mishandled.