Where does Linuxbrew globally binds $PATH?

I did remove linuxbrew, but still I got .linuxbrew in my $PATH. Where does linuxbrew sets the $PATH?

It doesn’t. It depends on users to add the necessary incantations to their shell startup files, so somewhere in the mists of time, you added PATH=...linuxbrew... to your ~/.bash_profile, or ~/.profile, or ~/.bashrc, or some other startup file specified in man <your_shell>.