The sentence seems to be wrong and it should be something like this:

Qualifying booking excludes a travel booking canceled by the traveler, or the one resulting from fraudulent or other illegal activity, for which we do not receive payment.

"We do not receive payment" refers to "booking canceled by the traveler" and to "fraudulent or other illegal activity."

There is an error in the sentence: instead of "we does not," it should be "we do not":

Qualifying booking excludes a travel booking canceled by the traveler, resulting from fraudulent or other illegal activity, or that we do not receive payment for.

"We do not receive payment" refers to any booking they do not receive payment for.

The sentence seems to be wrong and it should be something like this:

Qualifying booking excludes a travel booking canceled by the traveler, or the one resulting from fraudulent or other illegal activity, for which we do not receive payment.

"We do not receive payment" refers to "booking canceled by the traveler" and to "fraudulent or other illegal activity."

The sentence seems to be wrong and it should be something like this:

Qualifying booking excludes a travel booking canceled by the traveler, or the one resulting from fraudulent or other illegal activity, for which we do not receive payment.

"We do not receive payment" refers to "booking canceled by the traveler" and to "fraudulent or other illegal activity."