When we bought our TT late last year, that's the first thing we noticed that really bothered us. Personally, I think the basic design is poor.
What I did is buy an aluminum bracket that attaches to one end of the table and has a mating piece that attaches to the wall. It lifts into place and interlocks together. Not sure what it's called but I have seen it on Tweety's site or one of the other major vendor's sites. Then I bought a fold-out leg. I bought the leg and bracket at a local RV parts shop.
I removed the flanges under the table and on the floor. Since I was installing laminate flooring, I didn't have to worry about the holes left in the linoleum. You could just ignore the holes and use a little caulk. I supposed you could also remove some lino (if that's what you have) from an inconspicuous place like under a dinette bench and use it to patch the holes left from the flange. You might want to get a pro to do that.
The studs on the outside wall on our TT where I needed to attach the mounting bracket were not in the right location so I installed an oak ledger strip and stained it to match the cabinets. I added a length of oak to the end of the table to screw the bracket to. I also attached a square oak block under the table to attach the fold-out leg to. If you are careful and have the correct length screws, you probably don't need this. I used construction between my block and the table for added strength.
Now the table is rock solid.
Here are some photos. If there's anything I can add, just ask.