If your grout is not synthetic, vinegar and a stiff brush should work a hard tooth brush or even a nylon pot scrubber. You will have to put a little elbow grease into it. That could be tough.
Try a wire brush. Good luck.
D, if you click on "explore projects" then "clean" then "bathrooms" then "grout" you will find quite a lot of helpful hints and methods. I have chosen one for you, but there are many more. I hope one of them helps you. Good luck with spring cleaning! https://www.hometalk.com/23803774/how-to-clean-grout-and-install-new-grout-that-won-t-stain
Dremel works good if its a small job