"Triple thick" is referring to the "Trilaminar Endometrial Pattern" that FS look for prior to transfer. It's the triple layer pattern (or the "hamburger" as Wazza calls it).
It's something they like to see as it suggests the uterine lining has developed appropriately in response to increasing estrogen levels during your Cycle (as opposed to what they call a "Homogenous Endometrial Pattern"). It's also more favourable for achieving successful implantation in IVF or so the studies I've read tell me.
Ask her what your lining measures when she scans you for your upcoming FET. Ask her how many mm's it is on the day and can she see the "triple layer pattern"
Luv, in the IVF game, you soon learn you have to be your own advocate..doing your own research a lot of the time, asking the questions, suggesting treatment options/protocol changes etc unless you get a really pro-active and forward thinking, out of the box FS who will do it for you.
If not, you'll just get a FS who'll do the same old sh!t Cycle after Cycle after Cycle..they might only be willing to tweak a few minor things...and frankly, that just may not get you anywhere especially after 3/4/5 Cycles (stimulated cycles irrespective of transfers) of doing the same old, same old with no results or willingness to try anything different.
Disclaimer: Just my opinion