This is part of the divorce procedure - trying to settle the finances can be very difficult. What is supposed to happen is that you and your ex should make a full disclosure of your finances - all assets and liabilities and income - (on Court forms, I believe) and (through your soicitors) exchange the information. Any queries then have to be resolved if possible, and an agreement reached on how the assets are to be divided, as well as what maintenance is to be paid. If it is not possible to reach agreement the Court will decide.
Your solicitor should explain all this to you.
If you don't agree with your ex's proposal then you have to say so, & the Court will decide what is to happen if your ex takes the issue to Court.
I assume that by "for free" you mean handing the asset over without you getting any money in return. I think this is very unlikely, but no-one can tell you definitely. To some extent, it will depend on who has provided the deposit and made the mortgage payments but Courts take other factors into account as well.
Incidentally, you refer to your name being removed from the mortgage. That is a secondary issue. I assume the property in is both your names, & it is removal of your name from the title which is the main issue. However, it is possible your ex will not be able to get a mortgage in her sole name & that could lead to problems if the Court considers the property should be transferred to her.