Does not knowing the source of money make dealing with it forbidden?

The basic principle is that what is in a person's possession is their property, and this apparent ownership does not transfer except with certainty or strong circumstantial evidence. It is not obligatory to investigate the source of ownership. If there are strong indications that lead you to disbelieve that the deposit belongs to the person, then act accordingly and refrain from safeguarding it. If there is no strong indication and you safeguard it for a fee, then it is a condition that the fee be known, either as a fixed amount or a known portion of the deposit if the deposit itself is known.