This gets cited here weekly, usually second-hand, so it is worth setting out what it does and does not establish.
Routine calcitonin screening is not recommended and does more harm than good in this population — the false-positive rate is high and the workup is invasive. The rodent medullary thyroid carcinoma signal that drives the labelling has not translated into a human signal, but a personal or family history of MTC or MEN2 is a genuine contraindication rather than a formality. Separately, TSH is worth having at baseline because hypothyroidism explains fatigue that people will otherwise blame on the drug.
Where I think it is weakest: the subgroup findings are the part I trust least — with enough subgroups something is always significant, and these were not all pre-registered.
The narrow version of the question is why calcitonin screening is not recommended when the label carries a thyroid warning, because those two facts look contradictory from the outside. Practical detail welcome, however dull — the duller the better.
Note on sourcing:
Figures above are from the primary publication rather than the press summary. If a number here disagrees with one you have, post yours and we will work out which of us is reading a secondary source.