You can see some of their store items here www.911memorial.org/catalog These are what I've based my reflections on, so there may be items in the physical store at odds with these, please do let me know if you;re aware of anything else.
I went to a Titanic exhibition at the MOSI a good few years back, and was horribly jarred stepping from the room listing all the names of the dead, through to the gift shop. The issue there was in the main part going from a somber, well presented, touching area, directly into a brightly lit, brightly coloured, overly commercially aware space. There was also issue though with some rather odd choices of merchandise, such as the iceberg ice tray. Nice.
It looks as though the choices at the 9/11 site are there to help visitors further learn about the event, act as mementoes of their visit to a powerful site, and provide a form of support (the Virgil quote jewellery is especially touching)
There are some choices I find a little unusual, like a plush search and rescue dog, which feels like the product purchaser was trying to find something for small kids to demand from their parents. Largely though everything seems to match the themes of somber commemoration and pride in continuation, mixed in with that particularly American respect for their services (NYPD etc)
Design is a mix of tasteful graphics and photographs, remembering the site beforehand, icons selected as points for memorial, such as trees.
The money goes to help support the maintenance of the free memorial, subsidize the venue remaining open and provision of education and support, so it's not any form of fast buck.
Knowing that purchases help further their causes makes the carefully selected merchandise even more palatable. Their mission statements are as cheesy as one can expect from that ilk of thing, but understandably so.
May the lives remembered, the deeds recognized, and the spirit reawakened be eternal beacons, which reaffirm respect for life, strengthen our resolve to preserve freedom, and inspire an end to hatred, ignorance and intolerance.
I can't find much fault with the store as shown online, and the venue itself I can't comment on, if it offers a suitable space or jars as badly as Titanic did for me.
I expected to view the store online and feel disgusted or confused about product and design choices. Yet, leaving aside the issues around the museum itself, the merchandise seems wholly appropriate when you take a step back and switch gear mentally into 'American'.
If some of the choices in their store seem cash minded, remember that without irony, and more so than cold hearted commercialism, it's driven by genuine national pride and the desire to express solidarity with the victims both dead and living.