I purchased a gear lot of HSGI Taco pouches and it came with one first aid pouch.  While all the other gear I got is HSGI, I am not 100% sure on this bag.  It seems like it could be HSGI - same stitching, color, quality, and style, etc - but I don't see anything on their site that corresponds to it.  Still, I think it's likely HSGI brand.

Anyway, I think both of these items are part of the IFAK pouch - but I'd like to know how it's supposed to be used and packed.  The bag itself has both ends open, presumably to allow the IFAK to be pulled and removed from either side.  The bag has a center area and then a top and bottom area that have the attached straps as part of those.  The straps/pulls(?) seem to be attached to the top and bottom areas of the bag (not in the center channel).  There is no velcro on the pulls/straps.

The other bag looks like it would go inside the center channel and actually contain all the first aid items and then be held in place with the elastic pulls on the outside of the bag.  However, I don't know how this would pack in the bag, presumably to come out when one of the straps/pulls is pulled from either side?

Hopefully I'm explaining it well enough that someone can help point me in the right direction for setting this bag up properly.

Basically, you'd put the items inside the bag. You'd put the strap down inside the pouch so it lines the inside (with the edge hanging out), then put the bag in. To remove, you pull the strap hanging out and it all pops out. Small items, like NPAs and decomp needles, can go outside the pouch in the webbing. Or, you can attach a TQ holder there.

Most of these have a pretty limited capacity, mostly used for a belt option. I know HSGI has a bleeder pouch, but it doesn't have the insert, it's literally a pouch with a strap sewn to the inside (or at least, the older models do).

EDIT: Since the strap doesn't seem to be sewn down, you'd probably tie it to one of the D-rings on the bag. If there's a D-ring or similar on the inside of the pouch, you'd attach the other end there. That way you can pull it out but it's not completely separate from your body so if it pops out on accident you're not watching your medkit fall into a dark hole.

Found it!  HSGI NOLATAC M3T - Multi-Mission Medical Taco