I just learned that a relative is NOT related to the people that I thought were their parents. I discovered she is a child of another person, making her a grandchild instead of a child. How can I remove the link between her and the currently listed parents in order to insert her actual parents and then link the parent (her mother) to the grandparent (her father)?
On each Family page, there is an option under the Edit menu to "Change family members" .
Go first to the family where she does NOT belong and use this option to remove her. Then go to the page for the family where she DOES belong and select the option to add a child. It will allow you to search by name for the person you wish to add.
Note that this does not allow you to set the person's PEDIgree with her birth family (the way you can when you create a new child). If you want this, go to the edit menu for the person's Individual page and choose "Edit the raw GEDCOM". Find the block entitled "Family as a child:" and add another line that says 2 PEDI birth
The Family page is often overlooked (most can be done from Individuals page in webtrees) and it is exactly what you need. Just click on the link "Family with parents" to get there and then use the "Edit" menu.
Regarding that last issue (setting the pedigree) that can be done when you go to the person's tab Families and use the link "Link this individual to an existing family as a child".
In that dialog fill in the surnames of both parents to find the proper family, and you can set the pedigree in the same dialog.
I was using the "Change Family Members" option for years and was frustrated with absence of ability to set the pedigree (not often needed, but still) until I found that you could do the reverse.