Darryl's Gym Socks, as the name suggests, are gym socks worn by and belonging to Darryl McGee. Being the filthiest and most worn out socks in the McGee family household, having to wash them by hand is considered a punishment, especially to Scratch, who suggested it as such in Innocent Until Proven Ghostly and was almost given this very task as punishment when the evidence was against him after Pete and Sharon's Anniversary Cake had gone missing, but had that punishment taken away from him when Molly proved his innocence by revealing that carob--a key ingredient in the cake-- was something he can't eat on account of allergies.
When Geoff was revealed to be the real culprit, whether or not he was made to wash Darryl's Gym Socks is left up to debate with the fanbase.