Extensions / search request monetization

Hello

i own some chrome extension with few thousands of users.
i see many websites propose to monetize search requests by redirecting on bing. (very often through some "transparent" redirection on trovi)

I m already using this technic with a parter but:

i would like to implement myself this redirection/monetization to avoid this "man in the middle" and get full gains.

Any one know how this work in details ? (only to bing / not to yahoo search feeds)
I was supposing they used CJ affiliate program but i m quite stuck here ...

Thank you!
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