I assume the original booking was paid for by the corporate TA and you then paid for the upgrade?

To the extent there is anything due back for the underlying fare (taxes and third party fees) I imagine that should be due back to the TA.

The only element of the upgrade from WT-WTP which is due back to you personally is the extra APD if it was an exUK flight - the APD difference from WT to WTP is about £80 I think. The rest of the upgrade cost is not refundable as it is just the special fare promotion BA charged you to upgrade.

As to whether BA IT is sophisticated enough to split the refunds correctly between you and the TA that’s another story