I ran into that issue myself. I submitted a compound for NMR in DMSO-D6 and needed the compound back. Essential oils are usually somewhat volatile.

There are two things to try:

Try using clevenger apparatus. it is meant to extract volatile oils from the source material. it will work for DMSO as well

The suggested procedures by Dr Silver and Dr Devangi may be work well but, normally, essential oils are complex mixtures containing also partially water soluble components or with some polarity which cannot be extracted efficiently or may be retained in column during chromatography. I have some doubt that you may obtain an oil with the same original composition by extraction. 

Another procedure to eliminate DMSO is reverse osmosis but I'm not sure that it may be easily applied in this case. In any cases you may lost a part of your sample. And also the amount of the sample may have a role in the choose of the procedure to apply.

Let us wait for other contributions to this topic.

Preparatory or Thin layer chromatography can help you

I think option 1 from Jack Silver will run well and it will the easier way. Good luck.