What is the ruling on the ablution of someone who wipes over a short sock that reveals half of their heel when lifted to go to the mosque? And what is the permissible extent for the foot to be exposed from the sock without invalidating the ablution?

The majority of scholars hold that removing the khuff (leather sock) or the exposure of any part of the foot that must be washed invalidates the wiping and necessitates the renewal of ablution. Some scholars, however, do not consider the ablution invalidated by removing the khuff at all, and this is a strong opinion. Therefore, there is no objection to adopting the easier opinion in your situation, which many scholars permit after the act has occurred and rectification is difficult. However, if you wish to be on the safe side, you should repeat the prayers you performed with that ablution, as it is invalid according to the majority.