"How can she get this woman's name off her house...?" The problem presented in your question is that it is not solely "her house". Rather, the property belongs to both of them since the title to the property is held in both of their names.
If your friend is the only one paying the mortgage loan that both of them are legally responsible for (assuming the note is signed by both of them), and paying the taxes, insurance coverages, maintenance, etc., then your friend may have a basis to sue her former partner for her former partner's share of expenses. Such a lawsuit may trigger the motivation the former partner need to sign the quitclaim deed conveying your friend's and former partner's interests to only your friend, effectively extinguishing the former partner's interest in the property.
The lesson here is that before one grants an interest in one's property to someone else, you should carefully consider the natural consequences of doing so if the relationship later sours. One way to deal with this is by preparing and executing a written agreement that specifically sets forth what happens if one of the partners moves out or stops paying the mortgage loan, or refuses to contribute her share of the property taxes, insurance premiums, general maintenance (cutting the lawn, etc.). If you do not have a written agreement, then your agreement is as solid as the paper it is written on. If the property has equity, then I suspect that the former partner may not wish to walk away empty-handed, so convincing her to "get this woman's name off her house" may take a few dollars.
I recommend that your friend consult a litigator experienced in real estate disputes that can examine the deed and learn all of the facts to determine the viable options, and then your friend can select the option that makes the most sense to her. The lawyer will charge you an hourly rate and will require an initial retainer before he/she begins to dedicate time to the matter. I am happy to speak with your friend about this case, even if it is stoo small a matter for my firm to handle.
Good luck.
