Generally, even a non-Greats fighter can inflict an injury upon a Greats-level fighter if the non-Great is lucky enough to land a good hit on the Great. We saw it happen to Cheung Mo Gei multiple times in HSDS, and to his grandteacher Cheung 3 Fung as well when he was attacked by that faux Shaolin monk. In ROCH, Gwok Jing sustained injuries from the much weaker Lui Mor Singh and Siu Seung Tze as well as the Golden Wheel Monk, and in DGSD, Kiu Fung was wounded by weaker fighters who attacked him en masse at Tsui Yin Manor. Even the almighty Janitor Monk wasn't able to emerge completely unscathed when the relatively weaker Kiu Fung struck him with the Hong Lung 28 Palms.
When Ying Goo attacked Yeung Gor with her ice palms, however, she was unable to inflict any damage whatsoever. She probably could have done more damage by throwing a snowball at him (at least it would have gotten his shirt wet). Given this, I can only conclude that Ying Goo's ice palms must have really, really sucked (despite her having developed them over twenty years).