I've had three experiences in as many days that are making me rethink the
issue of giftpacks.

A new mother's (breastfeeding) aunt brought in a coupon from a magazine for one of those formula companies gift packs.  I told her we didn't carry formula gift packs anymore, and when she asked, I also told her why.  She asked, "Well what do you have to give a new mom?"

A father of a successfully breast feeding baby was enraged that we weren't sending him home with a case of formula, as we apparently had with his previoius infant.  We explained, one nurse after another, as well as the care partners (aides), the nurse practitioners and the doctors -- We explained that we no longer received the gift packs from the formula companies; and that this baby was not premature and severely jaundiced as was the previous one, and didn't need formula supplementation.  We even told him we could lose our jobs (RN's and aides) by giving him formula and possibly disrupting breast feeding.  Was he impressed?  No.  His response was that "for all the money he was paying for insurance (which actually his company paid for him), we could at least give him a couple of bottles of formula."

When moms leave the LDR area and come to postpartum, they are given a canvas bag (diaper bag size) that carries the supplies they'll need immediately postpartum -- the plastic bedside stuff, soap, mouthwash, rantex, pads etc.  The bag is imprinted with the Kaiser hospital logo.
One of the moms was looking in the bag and said "it would be nice if there was at least one thing for the baby in here."

So maybe we do need some kind of parting gift.  The baby, after all, they brought with them.  They're just carrying it home in a different wrapper than they carried it in in.  And the (hopefully excellent) care we give them they have paid for.  Maybe we could find appropriate things to give that not only acknowledge the fact that they just had a baby, but also say "Thanks for having your baby here."

Sincerely,  Chanita