It's pretty ironic that the princess is suspecting something is not right precisely because Rei insisted on the magic contract. If he had just made them swear on oath the old-fashioned way, they wouldn't have bothered to think about it nearly so much, thinking Rei is simply an adventurer who doesn't want to draw too much political attention or the attention of some scumbag who might be directly interested in Set for any reason imaginable. However, if one of them is more dishonest or simply an agent of an opposing faction, they would naturally spill all the beans, not caring for their honour in the slightest (because their honour lies in serving their real master). So, even if they hadn't thought as much of Set's abilities, it's possible someone else who heard the tales later would.
It's not an easy question, but as long as Rei doesn't care about making enemies or distancing friendly/neutral people from him (or the story is poorly written), it doesn't really matter if he uses the contract.