I am going to go over how to remove tags and the different options that you are given when removing a tag. Do the following to get to tags:
Click on Settings>Tags
You will see a list of tags on this page. From here you will be able to search for the tag you want to remove
Click the X on the tag and you will see the below pop up
These options are not reversible so be sure the correct option is selected before proceeding. Note: when you select the "Leave broken tag on contacts" you may be able to relink the contacts to the same tag when you recreate the tag with the exact same spelling and casing