Owe? The contracted price for the work (usually the cover/advertised price).
Requesting false, positive reviews... Demanding Removal of Negative reviews
(This does not mean a reviewer can't change their mind after an Author communication.)
What I
may offer of my own free will, is my opinion, reading recommendation (I used to sometimes
lend the paperback) to a friend who like similar type of work.
I don't even
owe the author an obligation to finish reading the book.