My mom is in the final stage of her terminal cancer. Basically we're providing her with palliative care at home. She started mumbling and moaning a lot last night. Its quite disturbing but she's not in pain. However everytime she falls asleep it happens.

Call the hospice nur. While some patients do moan in the last phase of life, i would ask the hospice nurse to assess her to see if you should try some extra pain medicine. Sometimes moaning is a non-verbal sign of pain, or delirium--both treatable conditions. But you probably need an experienced person to look at her.
Thank YOU. I have nothing to add to the other physicians, but i wanted to express my gratitude to you for caring for your mother, her good fortune in having you as caregiver. Remember to tell her that you love her, and keep doing this even if she seems to be unresponsive during waking hours. Blessings.
Your vignette. Doesn't pose a question, but hospice at home is helped by hospice providers that can ease your mom's final hours and help explain what is going on and how to help. Hospice does not mean a place, and itmeans the best of palliative care delivered by caring experts at yourr side helping you too.
Let her be/rest. This is very difficult to determine the best direction to go in. If she is not in pain, it might be best just to leave her alone. She is going through a lot and probably has a great deal to think about, not to mention the effects of her care. It night be good to talk with her about some of her possible concerns, etc., anything to help put here at ease. Spend as much time as you can with her.
May be expected... If she is unable to communicate and mumbling/moaning continues, this may be a condition we call terminal agitation. Depending on the team taking care of her, this can be managed with a medication such as haloperidol or lorazepam. If the team suspects pain (grimacing, furrowed brow & moaning) it's ok to start pain medication as well. If unsure, it's better to assume its pain rather than not.
Leave it. . If she seems comfortable, sleeping soundly and free of pain, then she should be left alone. It may be disturbing to watch but not for her to be experiencing. .