This didn't work since my local machine has a different python version from the remote (local: 3.10.x and remote: 3.6.5).

I don't know if it's ultimately going to work, but you can download the latest pylint compatible with python 3.6.5 explicitly, it's pylint 2.13.9 afaik so pip download "pylint==2.13.9".
I'm running vscode-server to develop on a remote machine via ssh. This machine has no connection to the internet and runs Python 3.6.5.
I would like to use pylint in vscode for the linting. Problem is that I cannot install it the normal way, since I don't have an internet connection.
What I tried so far:

Use pip download pylint, tar the resulting folder, move it via scp and install it on the remote machine. This didn't work since my local mchine has a different python version from the remote (local: 3.10.x and remote: 3.6.5).
Use the Install on remote: ssh button in the vscode marketplace. This succeeds but when I write code, a message pops up that says: Linter pylint is not installed. When I click on install, it just tries to execute pip install pylint on the remote, which will obviously fail...

Any suggestions on how to proceed here?
Getting Pylint to work with VSCode-Server