I found that even this, oddly, didn't work: when I pasted strikethrough-formatted text from Word into the About page on my website, Squarespace stripped out the strikethrough formatting. But I did find a workaround!
I typed the word I wanted struck through into one of my site's blog pages and used the strikethrough formatting button available on the blog page (but not available in About for some weird reason). Once Squarespace had formatted the strikethrough using whatever markup it uses, the formatting stuck when I pasted it into my About page.
Seems face-palmy to me: the functionality is everywhere, so why not just consistently use the same toolbar everywhere as well, instead of stripping out the button ...sometimes? Maybe it's just an oversight and they forgot to update all the toolbars when they added the feature, I dunno.