Can a laparoscopic incision site get infected and reopen 3-4 weeks post op?

Uncommon: Anything is possible but that is quite late for a wound infection to occur that late after surgery. See your surgeon asap.

Infected site: Any wound can reopen after a few weeks post op. Just because it was done laparoscopically doesn't preclude it from getting infected. Incisions are closed in layers and sometimes the area can get infected if the dressings got wet.

Yes: Certainly can-- may be related to surgery for infected organ e.G appendix etc but most likely this late would be reaction to suture material.

Unlikely: Its more likely there is a stitch trying to reach the surface and the wound may appear red and inflammed as its going to bit open.