No; the Bands are "worn" and thus come with
RAW
The misty step spell says only:
Briefly surrounded by silvery mist, you teleport up to 30 feet to an unoccupied space that you can see.
It does not, in fact, say that your clothes or other gear teleport with you, let alone anything magical that is restraining you - just you. This is odd, in that dimension door, for example, does say explicitly that you can bring what you are carrying. Spells do only what they say they do, so it is possible that dimension door allows you to bring gear (but you would remain bound by the iron bands) and misty step would free you of the bands but you would also be gearless and naked. Or, it could be that the gear provision is explicit but redundant in dimension door and implicit in misty step (and in teleport, for that matter). Fortunately there is an official ruling that clarifies this.
RAI, official
Sage Advice Compendium explains:
Misty step doesn’t say the caster can bring worn or carried equipment with them. Are they intended to leave everything, including their clothes, behind? No, the caster’s worn and carried equipment are intended to go with them.
Some teleportation effects do specify that you teleport with your gear; such specification is an example of a rule being needlessly fastidious, since no teleportation effect in the game assumes that you teleport without your clothes, just as the general movement rules don’t assume that you drop everything when you walk.
Here we have an explicit statement - the caster's worn and carried equipment are intended to go with them. So now the question becomes whether we should consider the iron bands to be "worn and carried equipment". This distinction is vague, but it is also key to adjudicating other spell effects.
Consider the part of the SAC ruling that says the "rules don’t assume that you drop everything when you walk." When a character moves, their gear remains with them. A creature restrained by the iron bands can't move, by definition - but it can be moved, for example by allies. If a character restrained by the iron bands was lifted up by a party member and carried away, would we expect the bands to fall off? Of course not. By the SAC definition, the bands appear to be "worn or carried". And while there is no in-game definition for what is "worn", certainly the English usage of the word includes a prisoner 'wearing' handcuffs, manacles, or other restraints. In fact, the Storm King's Thunder adventure (p. 181) includes precisely this use:
The non-ore prisoners wear manacles on their ankles that reduce their speed by 20 feet.
Thus, it seems clear that a discrete object that is retraining you, personally, fits the game sense of being "worn and carried". As such, misty step (like all teleport spells) is assumed to bring it with you.