The "powered by" usually shows up because the "add my referral link" options is checked when setting up the flight/hotels code.
You can uncheck that option on any TravelPayouts setup phase to make the "Powered by" text dissappears, because it only for referral thing, not affiliate thing.
Will I Still Get Paid If That Option Is Unchecked?
Yes because all your affiliate codes are automatically wrapped with your affiliate link (differentiate affiliate link with referral link).
With TravelPayouts you get 3 ways of making money:
[+] When someone make a book for flights tickets or hotel rooms
[+] When someone search for flights/hotel on your website and sign up (not even make a booking)
[+] When someone register to TravelPayouts affiliate program thru your referral link (that's what the "Add my referral link" option functions for)