Answer first: the class has documented effects on the gut hormone axis by design, and the claims that travel furthest are usually about axes it does not directly touch.
Ghrelin, peptide YY and glucagon-like peptide-1 itself all shift with sustained energy restriction, and those shifts partly oppose continued weight loss. That counter-regulation is a well-described phenomenon and is not specific to any drug.
To be exact about it, thyroid-stimulating hormone has a diurnal variation of a few tenths and a wide reference interval, so small movements within the interval are not findings.
The counter-regulatory hormonal response to weight loss is well documented in the physiological literature and persists for a long time after the loss itself.
Weight change moves several of these axes on its own, so attribution needs care.