Do I need to use paint or just cleaning agent for marks on kitchen wall?
Many paints "chalk", allowing surface dirt to be scrubbed off gently (e.g. with a weak solution of laundry detergent), but this also removes a very thin layer of paint. If cleaning changes the appearance noticeably, then repainting could be done.

Depending on the type of paint, no pretreatment might be necessary. Flat latex paint can often be reapplied after washing (to remove any surface dirt, e.g. evaporated cooking oil). Other paints are less forgiving, and might require sanding. See PaintInfo.com, This Old House, etc.