When you Pay with Points the full cost of the transaction is billed to your American Express account. You then redeem points to offset the charge. If you later cancel the transaction any refund should come to your card account, but (in my understanding) you cannot convert that credit back into points.
I just cancelled a pay with points hotel stay, and - consistent with mia's comment above - AMEX issued an $1800+ credit to my account rather than refunding the points. Anyone ever able to get the points back instead? I had lots of points to start, so it won't be the end of the world if the cash refund is final.