This Guardian article of Feb. 26 clears up some of this:

UNRWA's food parcels – which include tinned meat, rice and lentils – can feed a family of up to eight people for 10 days.

The agency is warning that the degradation of conditions inside the camp could lead to the spread of disease. There have been reports of mothers dying in childbirth, and families surviving on animal feed, according to a spokesman. The UN has sent in 10,000 doses of polio vaccine in the past month.

The UN security council adopted a resolution last week calling on all parties in Syria to take steps to facilitate the efforts of the UN and other humanitarian agencies to provide relief to civilians, "including by promptly facilitating safe and unhindered humanitarian access to populations in need of assistance in all areas under their control."

However, said Grandi, the situation on the ground was "very messy, very localised, a lot of local dynamics at play". Each distribution required "very complex negotiations with a lot of different groups".

and

United Nations workers have delivered about 7,000 food parcels over recent weeks, following negotiations between the Syrian government, rebel forces and Palestinian factions within the camp. The most recent delivery, of 450 parcels, was on Wednesday. The UN acknowledges that the level of aid is a "drop in the ocean".

Yarmouk has been cut off since last July. Many residents are now weak and severely malnourished, as well as being exposed to the risk of disease, or death and injury from fighting.

and

The distribution point is a "no-man's land", overlooked by sniper positions, between a Syrian government-controlled checkpoint and the camp's interior. "What about those who cannot come [to the distribution point]?" said Grandi. "I'm pretty sure there are many people who have never received assistance in the last month because they are too weak, or maybe elderly, or unaccompanied children."

Also note from the header:

has been under blockade for month

What is still not clear is the story of the picture if it was indeed taken on Jan. 31, i.e., how much aid was distributed that day, if any, or if they were lining up for like, some kind of registration or whatever. Because Jan. 31 is not reported anywhere as a date they managed to distribute some of the approx. 7,000 parcels they have distributed in total over the whole period. Because the U.N. knows it could not handle the vast needs in one trip, I can imagine them setting up a system where people get like a number and then that serves as a sort of queue. So that everyone does not have to line up again on every distribution the U.N. can manage to make.

Also,comes to mind when you are handing out parcels for a "family of 8 for 10 days" but cannot get in enough to aid all at once, you really do need some sort of I.D. process for fairness, to avoid black market type ops, to avoid only the fittest getting aid and then selling it or giving out unfairly?