We deployed the Tree Management Solution. It created many groups including the Tree Management Core Team group. It is a shared update group. "Members of this group can create, edit, and manage the site, pages, and other content related to Tree Management." - I interpret that to mean these users can modify the content, including lists on hosted feature layers. Is this correct?
The Tree Field Map uses the Trees hosted feature layer.
The user that I want to be able to modify these lists has the following privileges:

This is what the user sees when he tries to modify a list for the

What privilege does this user need to manage the list?