How to update mu-plugin

First, please check this out: https://codex.wordpress.org/Must_Use_Plugins

In most cases mu plugins consist of a singular php file in that directory. In that case you could just replace the file. In any case, there is neither a process for installation nor uninstallation, you simply drop files in that dir or delete them from it.

It’s as it is always with updates: Back the directory up, replace the plugin files one by one and check if everything’s still working as expected.

Never used the mu-plugins dir to store regular plugins. As e.g. activation hooks don’t fire in there, not every plugin is suitable to be put there. IF a regular plugin was put there, I would try to remove it (again, backup!) and install the latest version as you would any other.