For quite some time, the steam client is asking me to give them my mobile number. But I dont want that steam know it. So is there a possibility to tell steam to stop asking for my number?
It's a current bug and so you are not able to fix it right now.
What you can do is to get the newest beta version of the launcher, where it has been fixed already.
You can install the current beta version by choosing the beta client in the settings:
See also in this link.