Removing silicone damping fluid

Isopropyl alcohol (preferably 80% or higher) softens silicone, I've had to use it may times to remove silicone. Heat can also loosen it up so a heat gun or hair dryer can work, but is more dangerous to use. Of course you have to know what you can use where as alcohol and heat can't be used everywhere. Alcohol is great to use on metal or glass, but wood and plastics are a no-no.  

"Mineral spirits" is also mentioned in the owners pamphlet for the Townshend Audio Rock turntable (which employs silicon damping fluid in a trough for the arm/pickup) as the fluid to use for cleanup in case of spillage. Mineral spirits is a special version of petroleum-derived organic solvents, similar to naphtha and paint thinner, but free of some additives found in those chemicals. Other substitutes are denatured alcohol, acetone, and turpentine. Another interesting alternative is Orange Oil Natural Citrus Solvent.

@curiousjim - the fluid was supplied unbranded from Basis with the turntable, so I went to them for an answer. 

I’m no expert, but what does the manufacturer of the silicone say to use??

oil should be dissolve with soaps, no need to us solvents

I do not think there is any solvent for silicon fluids.

On silicon oil, I have used the most concentrated Dawn dish detergent I could find. Apply full strength, let it sit for a while and wash off with water, repeat if necessary. At least you aren't using any solvents that could ruin your TT.

FYI - for anyone in a similar situation, Basis recommended only a microfiber cloth with alcohol or simple green with water. I didn’t ask them about solvents and from their answer, I assume they don’t recommend any. 
BTW- they got back to me within 15 minutes. Great company for service.