I rebuilt the steering damper on m y old f800st, took it off the bike, cleaned it and then took it apart. Read the small numbers on the seals on the end, those numbers are the size and are used to order new parts, the o-ring inside you have to measure, as it might be worn also measure the bore of the damper, order a new one.
Buy some damper oil, i used 10w castrol fork tube oil.
Rebuild it , it is easy. There are no oem rebuild kits as Bmw only want to sell a new steering damper, but a rebuild is easy, quick and cost about 20usd with new seals and oil, the job is done with standard tools. There is no black magic involved and there are videos all over youtube, it does not have to be specificaly bmw dampers, all basic dampers function the same way. The adjustable ones are different but yours is not so.
Top tip is to not do the job inside the house, it can get a bit messy with the oil.......=)