M.L.
If I happened to be the mama in this scenario, I'd 'fess up. I'd call the other mothers and say, "I did a stupid thing! I lost the present list! We want to send you a thank-you note because I'm teaching my children how important it is to do that. Would you tell me what gifts you gave them? Can you see how red my face is over the phone as I ask you?"
And then I'd help the children write a brief thank-you, mentioning the gift by name.
You're not the first mother to misplace a list, and you want to teach your kids to be honest and aboveboard.
Your post remind me of an old story that's only distantly related, but maybe it'll make you feel a little better. There was a woman who let Christmas planning get away from her until the last week. She rushed around to get what she needed, including a box of Christmas cards which she liked the design of but didn't bother to look at the sentiment. She hurried home, scrawled a signature on every card in three minutes flat, addressed the cards in record time, stamped them, mailed them... and then went back home and noticed there was one card left over. She opened it up and it read: "This Christmas card/is just to say/a gift you'll love/is on the way."