if you mean the "Dirty Handkerchief" heres what you can do...
Location: Nacrene City
In the Café each day, the characters on the bottom floor will change. On Thursdays, the trainer who owns the mysterious "Dirty Handkerchief" will appear, where you can give them the item back. On Sunday, afterwards, you can speak to the waitress and receive the Fluffy Tail. -Source
if you mean the Dropped Item.
This item, when found, causes you to be in contact with the owner who will then request for it to be returned From there, you will be called when you enter random areas by the owner of the item. After the 10th call, the person will call you and tell you to meet in Nimbasa to return their Item. When you do, they will be added to your Xtransceiver. Call them to total 30 times, but you can only call from places which fulfill the conditions. On the 30th call they'll tell you they want to meet at Nimbasa City where they'll ride the Ferris Wheel with you. Call them to total 50 times, in the 40th call they'll be 'SOUND ONLY', in the 50th call they'll be wearing their work clothes, and cut the line in a second or so. Call them a 51st time. wait a day and then call them again and they'll meet you in Nimbasa City and offer to trade, willing to have any Pokémon. This can be repeated each day to go through all of their Pokémon. The Pokémon you receive varies based on your gender
The areas are as follows:
Behind the Pokemon Centre in Nimbasa City
Near the Officer in Route 16
Behind the fence on the bottom of Route 5
Somewhere near the slope to Clay Road in Driftveil City
Across the first bridge and near the ledges of Route 6
Around the stairs near the Breeder in Route 7
On the Airstrip of Mistralton City
Route 9 near the Hidden Hollow
Yamaji Town near the stairs.
Undella Town between 2 rocks
Route 13 near the start from Undella Town which is behind the ledge. Somewhere around there. There's rocks and a Fisherman. -Source