I have modified the holder to my requirements to make it independent of the thickness of the table and screw holes.
The diameter of the bracket I increased by 0.1mm.

For attaching to the table top, I recommend double-sided padded adhesive tape.

(Product example: https://www.amazon.de/dp/B016UUOZBI/ref=cm_sw_em_r_mt_dp_-HwMzbQBXSM00)

This thing was made with Tinkercad. Edit it online https://www.tinkercad.com/things/bjTL4lZ4lAr