I have been removing and re-fitting these CRT clips since the early 1970's.
For those it is best fold back the rubber cap edges, reach under the cap first, with thin long nosed pliers to squeeze the two pins together. Though if you understand the arrangement you can put force on the cap along the axis of the two spring pins, to compress them together, that way and aid the release of one of the side clips first.
Though I don't use any ordinary pliers, I always coat the metal of the pliers with plastic tape, the reason is you don't (ever) want a metal tool touching the glass-work of a CRT as it can scratch the glass.