Found this on quote on WetCanvas about oiling out a painting:

Oiling out with linseed oil before painting into a dried passage is preferable to using retouch varnish to resaturate the colors, from a standpoint of sound archival practice. Oils dry partly through oxidation, and varnish over the top of an uncured layer of oil paint inhibits its access to oxygen. One important consideration is to wipe or blot off as much of the oiling-out linseed oil as you can get off before painting into it. All that’s needed to accomplish the desired purpose is the absolute thinnest film possible. That will restore the colors to their wet appearance, lubricate the surface so the brush will glide smoothly, and aid the adhesion of the new paint with the previous layer. Linseed oil is chemically compatible with alkyd mediums. However, you might try painting without medium, just to simplify the chemistry of your paintings. Linseed oil can be added (via eyedropper for precise measurement) to each pile of paint that’s too stiff for good control, on the palette, and mixed in well with a palette knife. No turpentine is necessary. You might find this to work as well or better than your alkyd medium.

Secondly, the yellowing of linseed oil reverses itself in normal indoor lighting in a few years, and for that matter can be bleached out in a few days by placing the painting in outdoor light for a few hours a day. The yellowing does not return unless the painting is stored in the dark for extended periods of time, but this re-yellowing is also reversible in the same way. In fact, each cycle of yellowing and re-bleaching results in less yellow than there was before. Whereas the other oils, which make less durable paint films, also discolor slightly, over a longer period of years, and end up looking not much different from linseed oil paint films without the same degree of film strength. This can be seen on one of my test panels, and the phenomenon has been documented with scientific testing done by Henry Levison and others, the papers on which testing are in my files. Thus I see the often-expressed concerns over the yellowing of linseed oil as being largely unwarranted unless one far exceeds the amounts needed or sensible for sound technique.