Answer

This may depend on the question whether a perutah is one of the Torah’s legal minimum measures, or whether it is simply the definition of money. A practical difference would be whether stealing less than a perutah is considered a partial measure, or whether it is not considered money at all and therefore there is no theft here. According to the explanation that for less than a perutah’s worth Jews waive their claim, it seems that it is considered money, just that people waive it. But I seem to recall that in Rashi on Sanhedrin it implies that it is not considered money at all.
In any case, if people waive it, there is no obligation of payment, and simply speaking that is unrelated to the minimum measure of a perutah. But it seems that there is still a prohibition involved in any event.
Indeed, waiver can operate on a separate track parallel to the minimum measure / definition of money. So even if it is considered money, if people waive it there is no obligation to pay / return it. But simply speaking, there is still a prohibition involved.