It sounds like a donation was processed for Budget:XYZ in 2013, and a correction was processed in 2014 to change that 2013 donation to be for Other:AMFA:ABC. That created a 2014 transfer from Budget:XYZ to Other:AMFA:ABC. Let's just say the amount was $200. So you essentially have a 2014 charge of $200 to Budget:XYZ and a 2014 credit of $200 to Other:AMFA:ABC.
If that's the case (or something similar), then that means that the Budget balance carried forward into 2014 was artificially high by $200. It's true that there is no way to change the budget expenses for 2014, since any corrections you make will also be in 2014. But you could adjust the amount allocated to the Budget:XYZ. Perhaps that amount is $500. You can adjust that (using View/Edit Budget) to be $700. That will make the net balance available for Budget:XYZ (and for the overall Budget category) equal to what it would have been had you successfully processed the correction in 2013.
Of course, if you take this route, make sure that in your budget planning for 2015 that you factor in that both the budgeted amount and expenses for Budget:XYZ were artificially high by $200 during 2014. But other than that little detail, adjusting the budgeted amount for that subcategory should accomplish what you want.
Questions that can benefit the larger community should be asked in a public forum, not a private message.