Is it allowed to keep a Mutah marriage confidential if her father and grandfather are deceased, but her mother and brother are alive? Does she need their consent in this situation?
Bismihi ta'āla
In our Islamic tradition and culture, relationships are not just personal and individual. It is the coming together of two families. It should not be done in secrecy. That is a big red flag. How will he maintain his respect to her, if she's gone behind her family's back and done the most important thing in her life, without telling her family.
As is most cases, the male will definitely use this in a way that he will not show accountability to her family, and many other wrong things.
If she has not been married before, and even if she has been married, involving family is very important.
And Allah knows best