Wiktionary
dick's hatband
n. Something peculiar, extraordinary or incredible; usually used in phrases like queer as Dick's hatband or as tight as Dick's hatband.
Usage examples of "dick's hatband".
Hollo, thinks I, he ain't one of the Dick's hatband brigade, surely?
Tight as Dick's hatband, of course, but it proved how right I'd been to give her an encore.
After all, her only husband had been as fishy as Dick's hatband, by all accounts, and however many young stalwarts she'd whistled up since then, they wouldn't have my style.
Pounced on me, looking as queer as Dick's hatband, and wanting to know what the devil I meant by setting the Runners on to it.