Those of you familiar with this song: https://www.youtube.com/watch?v=6WTdTwcmxyo
may or may not know that it is pretty universally applicable as a phone lookup for most rewards cards. Just prefix with a popular area code, e.g. 415 (Bay Area) or 212 (NYC).
Naturally, you won't get any of the rewards, but it does protect your privacy, and with some annoying retailers, still gets you the member discount.