Assign vertex group doesn't work after first assignment.

I modelled a character and later an armature.
Now, I assigned an arm as a vertex group, and combined the armature.
But I saw that I selected a few bad faces and wanted to remove them, but reassigning doesn’t work:
The “select” (after deselecting) feature doesn’t work properly, it doesn’t select my assignments, but they worked because I see them moving as I pose my armature.

Later, I deleted the vertex group and added a new wan with the same name, but the armature data didn’t update. How can I do that?

Thanks for your support.

I got it, I think I didn’t assigned them well at the beginning.