Production for the movie began in 1983, and for test shots they used a Supergirl costume of their own design, which had a very contemporary look:
DC, for unknown reasons (but probably corporate synergy), decided to give that look to Supergirl in the comics as well:
The design first appeared without the headband in Supergirl #13 (September 1983), and then she made the headband in Supergirl #17 (January 1984). This wasn't a huge deal because Supergirl changed her costume all the time; readers could even submit their own designs that might make their way into the book. As you might have noticed, this costume is the one she wears on Crisis on Infinite Earths #7 (1985).
However, there's one hitch: by the time the movie started actual production, they had changed the costume!
Regardless, despite Supergirl not being nearly as successful as the Superman movies, it was able to leave its mark on the franchise as well.