What is the ruling on taking a portion of customer proceeds without the knowledge of the institution, in order to compensate for an amount deducted from one's salary in violation of a prior agreement?

It is not permissible for you to take the institution's money without their permission, as you are entrusted with it. The mere promise of the institution to pay the sponsorship transfer fees does not obligate them to do so, for the majority of scholars hold that fulfilling a promise is recommended, not obligatory. Furthermore, the one who promised you might not be authorized to do so.