Hooked rugs can be tricky to clean for two reasons:
1) They're made of so many mixed fabrics chances are good that at least one will not be color fast
2) The ground fabric is burlap which is weak enough already, and now it has been stressed for years with stretching (all those loops hooked through) and wear.
The usual way textile conservators clean them is to vacuum them through polyester screening, immerse in cleaning solution (usually neutral detergent like Orvus and maybe chelating agent like EDTA) while it is supported on semi-rigid polyester screening. It can be drained reasonably quickly by lifting the screening, then rinsed in at least 3 water baths, again by immersion and lifting.
Then it is transferred to towelling on a suction table and dried as quickly as possible, changing the towelling frequently.
That's the short version
So it's probably not something you want to undertake yourself, but it's always useful to be able to explain to client the general procedure that would be required should they wish to find a specialist.