It's not just you.
When Cyndi recorded the song 30 years ago, she was instructed to mimic Christine McVie to the best of her ability. She was just one of several session singers hired to re-record several big hits of the day. Clearly, some additional knob-turning was done to adjust her vocal. Also, all the trademark Lauper vocal ticks, affectations, and cartoonish-singing-through-the-nose quirkiness didn't come until later.
A 7" vinyl single was the only release from the session. Details about the release are unknown even to Lauper herself, who did not own her own copy until a fan gave her one in 2002. Lauper then remarked she was paid only twelve dollars for her work, to "sound like someone else."
After Lauper's later success, a 12" vinyl single featuring new remixes was released in Japan in 1984 on a small independent label called Jam Spot, which was a division of Yamano Music Co. In 1989, a 3" CD single also surfaced in Japan with the same mixes. All of these versions are considered rarities in Lauper's catalogue.
I've seen this track listed on every Cyndi website, timeline, and discography but I'd never heard it until this week.
