Make a <library-name>.d.ts file somewhere in your repo, and make its contents be `declare module 'library-name';`. This will make Typescript treat the library and all of its exports as any-typed. If you find it useful to, over time you can fill in the .d.ts file with actual type information, and then maybe submit it to DefinitelyTyped when you think it's complete.
They almost all do if you look hard enough, but it there really isn't one this is one of those edge cases where it's ok to generally just define it as an 'any' and save yourself some hurt.
It's that or take the time to make it yourself, but it might not be worth the effort, it's for you to judge.
Lose it or fix it (e.g. by writing some type definitions). If either is infeasible, put a fence around it and surround it with some layer. Most common libraries have type definitions at this point. The better ones actually maintain those themselves.