<Usual caveat that Chief Delphi in general is not and I in particular am not an official source>
As I read it, the key item here is the last sentence of G15, shown in bold:
A hook is clearly a “robot part”. Intentionally detaching it on a string or similar not-even-close-to-rigid tether is against the rules “unless permitted by a Game Specific Rule”. Remember, the boxes are intended to clarify the actual rules - in this case the rule answers the question directly, and the box is apparently for emphasis.
If that hook were on, say, a telescoping antenna or tool handle which was at least nominally rigid? I’d guess it was legal, but would definitely check Q&A or have a plan B to put in place at competition were I planning to do it.