The car jerking came back several months after my last posting here.
Lately in addition to this jerking some strange sounds started to appear. The sounds like crackle of a cardboard or plastic bag under the tires . I took it to mechanic. He drove tested and stated that between 3-rd and 4-th gear the trany disks slips.
I took my TL to another mechanic shop where they drive tested with the computer attached. The result - serious problem with the trany.
So I just bought 2 days ago used trany with 42K on it. Next week am taking my TL to mechanic to swap the trany.

I heard that there is a way to get from Honda compensation for the trany exchange. I would really appreciate some hints.