This is an old thread, but it was helpful to me.
An internet search on this problem yields this forum discussion, and others. The following article from cars.com shows the problem continued for years, even after this thread was started:
https://www.cars.com/articles/2011-2015-lexus-ct-200h-door-pull-issue-1420683170804/
I called the main Lexus number (1-800-255-3987), explained the problem and also informed two of their phone representatives that this was a known design issue. They claimed not to have any knowledge of this issue, and said they couldn't do anything, unless I was willing to drive to a Lexus dealership and have them inspect it. They didn't care that I could give them the TSB reference No. SB0037-22R2.
Instead of wasting my time driving to the dealership (45 minute drive, plus unknown waiting and insincere discussion time), I just bought the part for $35 off of eBay. It was delivered earlier today and snapped in place with no problem.
I recommend doing as I did. You can search on eBay (or elsewhere) for Lexus part number 74645-76010-C1. It might be described as a "front right door interior trim cover," or as a "door assist grip cover." The new part is built with thicker clear plastic clips, which replaced the flimsy and bendable metal clips, which used to pop out. I paid a total of $35 with shipping, and received it in under a week. (You might find it cheaper?) Now I'm happy, because I no longer will be embarrassed, driving a car that falls apart whenever my passenger shuts the door.
Very disappointed with Lexus regarding this issue. Clearly, they know about the problem (it's all over the internet), but their representatives pretend there's nothing wrong.
My car is a 2013 model, bought "certified pre-owned" from the local Serramonte dealership (northern California) in 2015. I have been snapping the original piece back in, repeatedly, since I purchased it.