Kitchen sink overflow pipe too long?
There would certainly be no problem shortening the flexible pipe some so that it does not collect water at its low point. Before cutting though make sure you comprehend the type of fitting used to join that pipe to the right side sink drain basket. (There may be a need to have new parts if a portion is not re-usable).

It is not possible to tell from your picture if there is a properly installed P-trap in the main drain line. Note that the P-trap also keeps some water to seal the drain off so that sewer gas does not come up into the sink. If that trap is installed incorrectly or of there is not a properly installed vent pipe on the down flow side of the trap there is a possibility that the bad smell that you are experiencing may not come from the overflow pipe. 

So I would first suggest to shorten the overflow pipe and then clean/sanitize the drain system, including the overflow pipe. Then you can re-evaluate to see if there is still a bad odor in the drains. If so you would then need to have the apartment folks come back and correct the possible trap problems.