I just removed, cleaned and swapped the covers between my dead SE and my current Sport (both 2003 TJs).
The foam is more dense and hard than what you see in bicycling helmets. It is like a really soft plastic. It has all sorts of hard plastic inserts and tabs to allow it to adhere to the roll cage. They mostly are like typical "christmas tree" push-in plugs like used to hold the inner fender wells in place.
The covers zip on and off, but are a PITA to initially get oriented. I ended up zipping one rear leg to see how it would end up being shaped and figured it all out from that.
The front door pads and covers are separate from the rest. The roll cage is one huge and ungainly cover.
The easiest way (after doing two complete sets) was to remove the sound pods. Unclip the wiring harnesses and yank them from the top bar. They have a 1.5" to 2" long threaded rod sticking into the top bar. This is inserted into a long, rubber grommet. Pull the rubber grommet and stick it over the threaded rod. This is a lot easier to assemble than to try and shove the threaded rod into the rubber grommet when it is already on the bar. Don't know why. It just was for us.
The bos for the sot top must be detached. It is easier to remove the small phillips head screw in each plastic plug that connects each bow to the bar. The plug is attached to its swivel point on the bar very tightly, but the screw comes out easily and the bow pulls off easily from the plug.
We then shoved the entire top and the bows over the windshield so that it was flopping down onto the hood. This gives you lots of room to work on the stupid covers.
We tried several ways of removing and reinstalling these covers. The best way seemed to be to get it oriented first. Again, we zipped up one rear sleeve to see how it was shaped and that gave us the right and left of the thing.
Unzip it and wrap one rear leg around the rear of the bar at the bottom. Center the zipper so that it is to the rear or top of the bar, along the center line. Set it so that it is lightly in contact with the plastic seatbelt tensioner cover.
Zip it up to the cross bar at the top all the way to the end of the zipper. Tuck the zipper end inside the cover.
Do the other side the same way.
Now zip up the vertical side bars, starting at the bottom. The zipper should now be automatically oriented correctly. Fit the cover over the two soft top black plastic plugs. Be careful to not tear the fabric. It is tight but it does fit. Make sure that the holes for the sound pod screws are accessible through the holes in the cover.
Same as before, tuck the end of the zipper into the cover.
Now you need to zip up the top bar. Make certain that it is not twisted. You have four holes for the sound pods. Two are for the wires, and two are to receive those rubber grommets on the threaded rods. The cover must be clear of these four holes. Tuck the zipper into the cover again. Then do up the velcro tabs that cover up all the "joints" and zipper ends.
Place the two screws into their holes on one of the sound pods. Place it on the side bar with a corner on the top bar and reconnect the wiring. Stuff the rubber grommet into the hole. Hammer it into place until it seats. (I used my hand for the first two and then a black rubber mallet for the other two.)
When the grommet is seated connect the screws, jiggling the pod as needed to get things lined up properly. Once torqued down pretty snugly the pod is pretty rigidly held in place.
Drag the soft top back over the roll bar and reconnect the hoops to the plugs with the screws you removed earlier.
Install the top. (Or put it down. Whatever.). You are done.
We were able to stitch up several tears and wash the covers with them off. Much better!