So now I have two advices - to separate the tape from the screen - leave it on the bezel
or to separate it from the bezel - leave it on the screen.
I hoped to leave this decision to a chance - whichever it goes.
I doubt if at the initial stage - to begin the separation - there is a gap wide enough to reach to help that separation with a tool. But when I tried a few days ago, it did not start by itself either.
I did use a guitar pick to begin the separation of the bezel from the case, though. Then I continued with a plastic card.
I disengaged all four sides successfully and then after closing there is no damage done. Not as in some pictures where a metal tool was used.