I don't envy your position in accepting to do the treatment to be honest. You will have to be so careful not to disrupt the extensions.
I don't used any oils ,nor massage balms on the scalp as the fingertips and hands do the gliding and pressure points. What small amount gets onto the hair is from the other areas treated in your treatment, if that makes sense.
Upper back, shoulders, decollete and face I would use a massage balm or cream as opposed to an oil in this situation. It is less likely to soak into the hair.
Kaeso do a lovely massage sorbet which is very nice and won't soak into the hair.
Proceed very carefully using fingertip pressure , minimal gliding etc. However if you find it is too tricky on the scalp, tell the client it cannot be done because of them. Let's face it you don't end up paying out for the extensions because you've messed them up.
Spend more time in the other areas and stick to just pressure points for the scalp if it's difficult.
Good luck, let me know how you go on .