I just watched the TIF procedure online, since I wasn't familiar with it. It sounds really interesting. I didn't go that route--rather had the Nissen surgery. From what I saw, although you didn't have any cutting, your esophagus/stomach underwent a big restructuring. There are sutures, etc, that can cause swelling. Swelling in certain areas can open spaces in the new valve that can allow some reflux. Also, as I was told, the esophagus can interpret any discomfort as "reflux", since it's a "dumb organ" and can't differentiate between various discomforts.
Also, you're only four weeks out. At this time in your recovery (if it's anything like the Nissen recovery--and i don't see that it's all that different, minus the laproscopic surgical piece) pretty much anything can happen. Things are still in the early stages of healing.
Try not to overreact to those "reflux" feelings. Many people who are recovering from GERD surgery get them, and all of them worry that their wrap didn't work. Not true. Give yourself time to heal completely.
Best wishes for a great outcome! Be patient!