Will I be burdened with sin regarding a sum of money that was supposed to be returned to an aggrieved client, knowing that I did not fail to remind the company owner of this during my time managing it?

The apparent meaning of the question is that the questioner did not fall short in his work, and the delay is on the part of the owner. The principle is that this amount is binding upon the company, not its manager. The client can refer to the company and demand his right if he has one.