Found it, thanks.
I couldn't edit the string in the language file to translate to nothing because then that would display:
[website] %s (f.e. "mydomain 2") and it doesn't make sense.
I had to edit the default template file, exactly as you suggested, in order to display correctly that information.
In case someone else needs this, it is in
root/components/com_comprofiler/plugin/templates/[template name, usually "default"]/default.php
around line 370.
Ευχαριστώ krileon