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"I thought they have the right to ask for service they pay for
and naturally I have the duty to do a service for their satisfaction."
How about this: '(I think) they have the right to receive the service they pay for, and (naturally)(of course) I must provide that service to their satisfaction.'
This way makes perfect sense to me:
"I thought they had the right to ask for the service they paid for
and naturally I had the duty to do a service for their satisfaction"