There was no mistaking that jaunty walk.

[tufguy]

There was no mistaking that jaunty walk.

I couldn't understand this part "no mistaking that". Could you please help. I think the usage is weird for me.

Can we say "there was no mistaking that he was a thief"?

 

[Raymott]

There was no mistaking [that jaunty walk.]
"No mistaking" doesn't belong with "that jaunty walk". 'That' is not a relative pronoun; it's a determiner.
A: "What jaunty walk?"
B: "That jaunty walk!"

It appears to mean that there is no mistaking who that jaunty walk belongs to. "There's no mistaking that jaunty walk. That is Jaunty Jake."

Yes, you can use that thief sentence.