  We observe that O'Grady's birational maps between moduli of sheaves on an
elliptic K3 surface can be interpreted as intermediate wall-crossing
(wall-hitting) transformations at the so-called totally semistable walls,
studied by Bayer and Macr\`i. As an ingredient to prove this observation, we
describe the first totally semistable wall for ideal sheaves of $n$ points on
the elliptic K3. We then use this observation to make a remark on Marian and
Oprea's strange duality.
