Anyone who has been a professional massage therapist for any length of time knows that after a while their massage towels will begin to smell a little rancid. This is regardless of how fastidious and diligent they are with respect to washing their towels. They will try to wash them hot, try to wash them cold and use various proprietary products in an attempt to rid them of the all pervasive smell.
Any time they go for a massage with another therapist then they will be highly attuned to how their towels smell and will be immediately aware of any rancid smell.
If you go visit any massage forum and search for questions regarding the rancid smell in massage towels then there will be a plethora of potential solutions that you may be willing to try. Some of these may work; some may not be as effective.
Some of the solutions are based on changing the carrier oil you use for your massage and coconut oils are frequently suggested.
However, a simple method that I have found effective for my towels is to add some normal washing up liquid to hot water in the bath and soak the towels for an hour or so. Adding a few drops of tea-tree oil has been suggested to me. When the water has cooled a little then, with bare feet, stomp on the towels for a few minutes as though you are crushing grapes (can be quite therapeutic by itself or a job for the children).
There is no need to do this again until such time as the towels show the first signs of starting to smell.