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The phrase "acknowledge the debt" is correct and usable in written English.
You can use it when discussing financial obligations or recognizing a responsibility to repay borrowed money.
Example: "In order to maintain a good relationship with our creditors, we must acknowledge the debt we owe them."
Alternatives: "recognize the obligation" or "admit the liability."
Exact(23)
Hockney would later acknowledge the debt he owed to Stafford.
In that connection, it is important to acknowledge the debt we owe President Bush.
The most one can hope is that they acknowledge the debt.
Maurice would, and did, gladly acknowledge the debt he owed to Helen and the joy they had shared with their three children, Robert, Juliet and Edmund.
Mutu, though is reflective enough also to acknowledge the debt he owes to Fabio Capello, the coach who was prepared to offer him a second chance.
And let us acknowledge the debt which our modern conception of human rights owes to the teachings and traditions of the Christian church".
Similar(37)
Obama acknowledged the debt.
Abramović was brought to tears, while he wordlessly acknowledged the debt he owed his subject.
Robinson always acknowledged the debt he and the United States owed to Owens and, in particular, Louis.
His austere citizenly dedication inspired the young Ralph Nader, who has acknowledged the debt.
Mr. Lee's lawyer, Dino J. Lombardi, acknowledges the debt and said it was being paid down.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com