To remove mine, I simply drilled out the teak plugs and then removed the screws. I now actually have not put in new plugs so that I can now simply remove the screws, slide the hatch forward under the traveler and remove it to do maintenance varnish coats when I need to. See the pic. Drill out plugs and remove screws indicated by small arrows. Remove the aft section of teak. Slide hatch forward under traveler to remove. No need the remove traveler.
I tried this without thinking, and realized I had another problem: a previous owner had installed a deck organizer near the mast, which prevents the hatch from being able to slide all the way.
So I tried doing it the other way: I removed the screws from the fore side of the hatch too, and it slid off to aft. Removing the aft part served no real purpose, but it might give me the chance to attack some rot taking hold there.
But in doing so, I noticed something else. The teak ridge on the top of my hatch does not fit under my traveler, even the base of your traveler looks remarkably similar. The legs on mind are much shorter, and even have a peice of marine plywood raising the traveler an inch higher so it barely clears the top itself. I think one or both of our travelers are not stock; since yours is nicer, I'm guessing yours. So even if I hadn't had the conflict with the teck organizer, I would have had a conflict with the traveller. In my instance, it's super-easy to take the traveler rail off, if it had come to that.
I discovered I didn't particularly like Don Casey's method of bung removal: screwing in a screw, and keep turning. I aborted after trying just one, because it seemed as likely to destroy that entire part of the wood as anything else. I ended up underdrilling and then using a dremel tool to clean up. The fore end seemed in worse shape that the aft: the bung spacing is irregular; three of the bungs had larger screws than the others, one screw broke while screwing it out, and one bung didn't seem to have anything underneath it at all. It appears that the bungs were glued in with epoxy, or something similarly-colored, as I had to scratch it out of the screwheads.
Pulling off the end peice wasn't so bad, probably assisted by the water instrusion, but it's not that pretty, pulling off about as much wood as it did glue. I can't imagine ever signing up to doing this again; as long as the protected parts of it pass inspection tomorrow, I'm going forward under the assumption that all of the bungs are going back in, etc. Leaving exposed fasteners seems like a bad idea in any case, if water can get around them, varnish or no varnish. This happened to a few of my screws, and they didn't screw out so much as they were pulled out.