That is an agreement made between Palace and the county FA as FA rules state that all clubs must take part in the County Cup relevant to their position ie in this case The Surrey Senior Cup, as BHA do the Sussex Senior Cup but Palace said some years ago that they didnt want to play a youth team...
In the past Palace have always affiliated to Surrey FA not London FA but Wimbledon when they shared Shithurst Park affiliated to London FA, not sure if that is still the same now.