Whether or not there is a transfer tax/recording tax depends on what state the property is in. There's good reason why we asked that. You weren't supposed to just delete it.
Given the value of the gift exceeds $15,000, you will need to file a gift tax return, but no tax is likely due unless the property is worth millions.
There's no reason a non-PR can't own property in the US. Nothing happens just because she gives up (or otherwise loses) her PR status.
What makes you think she will ever give you the property back if you give it to her? What is your motivation in giving it to her? If she remains a PR, gifting the property back may disqualify her for certain services. Once you give it to her, she's free to sell it and you can't do anything about it. Also, if there is a mortgage on the property, it will be subject to being called by this transfer.

