You're right that we need to prove our competence. Note, however, that the most important element of that is actually being successful in our task. And that particular mission is by far the hardest.
Let's assume the noble simply refuses to pay, no matter what we say or how many of his associates we charm to talk to him on our behalf. What are we going to do? We won't be able to do anything. Not without causing repercussions for Gorthos he will not be pleased with.
We can take this mission later, when we've already done 1 or 2 other jobs, and done them well. At that point, should we fail, Gorthos will probably shrug and go "oh well, it was a long shot". But if we fail now, at our first task, he will almost certainly ask himself "come to think of it, why did I let this young braggart stay again?". And then he will find that he can think of no reason.
Never gamble. Unless you have no other options. In this case, we do have other options.