I have one of the "waffle" type pads under my dining table.
I understand there are ones that can leave marks. I purchased mine with the rug and do not see any problems. However, I do have a pad under the rug in the foyer. While I do not notice any marks, it sometimes sticks to the floor. I am sure I should replace it with something better.
I just ordered a seagrass rug for my bedroom and it was recommended that I put a pad underneath as even with the latex, it might scratch through onto the floor. I have a sample and the latex is pretty thin. I ordered from the same company who is making the rug - I have not yet received it.

That's one of those "It certainly can't hurt" kinds of things, I think.

I was concerned that a pad under the latex-backed seagrass rug might make it too thick and become a tripping hazard.

At least on the one I have ordered, the latex backing is very thin.
I think that is one of the reasons they recommend another pad - so the seagrass doesn't poke through the latex and scratch the floor. When I ordered the rug, my decorator also said to make sure I ordered a pad for underneath - for the same reasons.
I had not thought about felt backing - but mine is one 3'6" x 5'6", so I am thinking that felt might slide.

I have Saltillo tile floors throughout my house now, and a rug pad was a definite concern for me for leaving waffle marks. I ordered my rug pads from The Rug Corner-so look into them. They are very well made and more expensive, but seem to be totally worth it now that I have them. They feel so much better under the rugs than the thin ones anyway-just be careful of door openings to make sure the door can open across the rug if need be, because they are thicker.

I will say, I have had wood floors for many years before getting the Saltillo tile floors, and I never had a problem with the latex rug pads.

I think the problem lies, especially on Saltillo tile and heated floors, the latex melts onto the floor, which has happened to me in a small area and I could not remove it.

I have a seagrass run in my family room with HW with a felt pad beneath (we had it there from the prior rug). It's not quite to size, so there is a ridge in the rug where it begins. I would not recommend this under a table/chairs for this reason.

I've had waffle pads under smaller rugs, and have not had problems with damage to HW floors. But if your concern is the scratching from the seagrass, if a piece pokes through the latex backing of the rug itself, it may very well poke through the pad, especially with chairs moving back and forth across it. But I would take this over a felt pad under your table.