A mucous cysts on the finger, just below the cuticle, is not uncommon. It is a sac-like structure that is filled with fluid and it can cause the finger nail to become indented. It can also cause pain, particularly if there is arthritis or osteophyte formation (small bone pieces) in the joint.
There are ways to treat the cysts without surgery, such as with steroid injections, but they are not always successful and the cyst may come back. Surgery is more reliable in terms of long-term results, but all surgery has its risks, such as infection.
Whether your mother should take the risk or not is a discussion she should have with her doctor, who knows her medical history. Second opinions are also possible and if your mother has questions or doubts, then she should consider consulting with another physician.