They arrived at Mr Tarit's house in Rangsit area on more than 20 vehicles, led by Chumpol Julasai, Putthipong Punnakant and Sakonthi Pattiyakul.
Speaking through loudspeakers, the protesters called for Mr Tarit to take up the cases filed against red-shirts who put up signboards and banners in the name of Sor Por Por Lanna as special cases.
They also demanded the DSI chief adhere to justice in handling various cases.
Mr Tarit's house was protected by a number of police.
The protesters, after a brief visit, moved from Mr Tarit's house to an unannounced destination.