I don't know about the Courtyard but you can at the Grosvenor. The lady I spoke with said they could drop either the first or last day off when purchasing. (I know you didn't ask but I found this info out while putting together some info for a friend).
I'll also add the Grosvenor has gotten mixed reviews. I stayed there using Priceline last June for 10 nights. My son & I loved it. I'd like to go back.
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