Given that the report says “climbing through FL320” suggests they did stop the climb once other, more important tasks had been completed. One assumes this happened over the channel in the climb out - a very busy piece of airspace with aircraft climbing and descending through all levels on an FIR boundary.
Quite why every tiny detail has to be scrutinised in a way akin to petty phallus waving, I’ve no idea. They diagnosed the problem, ran the procedures and returned for a safe landing. Job done. The aircraft was never in danger continuing the climb.