I'd start with the mildest cleaning method and work up to harsher methods only as required.
First off I'd try a soft toothbrush and a mild cleaner like Murphy's Oil Soap. Rinse with water, pat the excess wood off with a towel, and let the grip dry s-l-o-w-l-y, perhaps even loosely wrapped in plastic so it doesn't dry too fast.
If there's some sort of varnish on the grips, acetone may strip it off. Follow up with the Murphy's Oil Soap wash.
Whatever you do, don't try oven cleaner which is sometimes recommended to clean up military rifle stocks! (Sometimes military wood rifle stocks respond well to a cycle in the dishwasher, but I'd be reluctant to try this method on thin pistol grips.)
Rub in a thin coat of boiled linseed oil afterwards.
To be kind to your enemy is to be cruel to yourself - Sun Tzu