"Leave the gear down"? Why? How do you know a tyre has burst? Yes - there are TPIs on the Flt Deck but they are really for maint purposes and about the most unreliable eqpt fitted (most of our Airbus ones currently disabled).
NB "leaving the gear down" on a MTOW jet = invalid performance in case of engine failure (if you have to leave the gear down e.g. brake unit U/S your MTOW is limited based on climb perf).
Proceed to dest? Well, it's pretty clear the manual says fine if no further indication.
In short 2 decisions to make:
1 short term, and I would be most concerned if there was a decision to leave the gear down, outside the SOPs, that compromised takeoff perf.
1 long term - proceed? It would take an hour+ to decide "what" went wrong (as they say, info they later got was vague anyway), dump fuel to as light as possible etc. Might as well continue en route with suitable divs. Later becomes apparent no further issues, continue seems fine.
To me, the most likely reason to return was the company considering damage needing to be repaired, and facilities at dest. This is a commercial decision, and in the days of modern comms, would be "requested" from outside the Flt Deck. Up to the Flt Crew whether they then followed that, and how (and to an extent same for a decison to continue).
Each of those advocting a return is doing so
outside the SOPs. This is perfectly OK, but might need to be justified
