1.   Oil might soften the paint but would mess up the paper badly, and the oil would stay forever.

2.   Oil will soften everything but stone or metal.

3.   Oil will soften almost anything.

4.   The oil treatment should have worked because oil will soften anything.

5.   The oil will soften the paint enough so it can be wiped off.

6.   The oil may soften the varnish just a bit so it can be sort of reworked and smoothed out as you rub.