Note that although the list was collected at Ellis Island, it was originally produced at the other end, by the shipping company. This is why you sometimes see entries on the shipping list crossed through - the company made a list up of those who had booked passage, then crossed through those who did not sail for some reason. The shipping company did their best to pre-exclude anyone who the US authorities might deport, seeing as they'd be paying for the return journey if they did get deported. (Same reason your airline checks if you need a visa when you check in).
The Keanes have "Under 16" marked, also "section 11" which I think might relate to this:
Section 11 provides that if a helpless alien is accompanied by
a person whose guardianship is necessary to him, the shipper shall
be required to return the guardian together with the helpless alien
when deported.
That is, the youngest sibling was held because they were younger than 16 and not accompanied by or heading to stay with their parent(s). The others were held under "section 11" because if it was decided that the youngest sibling couldn't enter the country, they couldn't just deport an eleven year old by themselves.
You'll see that others on the same list with Sec 11/Under 16 marked include a family where the man's 15 year old brother travelled with them, and the aunt of two underage children. Presumably in most of these cases either the parents were deceased or had given permission for the child to go abroad - the Keanes weren't held for long, so I guess they were just establishing that the eldest brother was the legal guardian and could provide for her.