This is a difficult situation, as even though an Owners Corporation (O/C) can, by Special Resolution, decide not to maintain items such as trees (now large) originally planted by Proprietors, that’s only possible so long as that decision “will not affect the safety of any building, structure or common property”.
So whether the courtyards are Common Property or part of the Lots, the Strata Manager must have judged the tree to be a threat to a building/structure etc, and additionally as it would almost certainly been outside the stratum of the Lot (i.e. distances shown on the Title Plan above and below a fixed reference point such as the raft slab of the townhouse/s) its the O/C’s responsibility on that count also.
That’s why the Strata Managers arranged for its removal, and that’s also why they should now arrange and pay for the pest inspection and for any termite treatment necessary.