I am refinishing a 50 year old salad bowl. It is carved out of
a solid piece of wood. The end grain runs along the length of it.

Where the finish wore off in the end grain area, the grain is filled with
olive oil. The salad bowl finish looks great, but will not dry over the
contaminated end grains.

I have soaked it in soapy water, and the oil comes off. I wait till it
drys(the water)
and it seems like it is ready to apply the finish, but the old oils seep out
again.

What can I use to clean this well enough to allow the finish to dry?