You can't push your modifications to a submodule you don't own.

Also, you can only remove a submodule manually. There's no option to have git do it for you.

The first thing you should do is fork the repository and set up a remote for pulling in upstream changes.

There are a lot of useful libraries out there, but I find I occasionally need to make changes. Sometimes there are bugs; sometimes the maintainer has lost interest. I need to be able to pick up the slack when that happens.

Regarding pushing modifications: Why not fork the submodule to your own remote? That's what we do.