I've been under many, many, many oily masseuses!
In my early days of FBSM, I too was worried about bringing tell-tale smells back home ... and would regularly check with any SP that the oil they were going to use was unscented. With time, I no longer bother ... and have enjoyed a variety of oils - thin, thick, scented, seeded ... knowing that I'll have a thorough shower afterward.
So, the bottom line is that you absolutely must have a shower afterward.For me, the more worrying tell-tale signs are from my sudden and unusual super-smooth and ultra-silky bodily skin, although this has not yet arose suspicion from my OH, when she snuggles up ... and moreover scented and girly shower/shampoo gels! Usually, astute SPs provide neutral or manly gels ... but there have been rare times where there's been nothing to use but a fucking flowery gel, which leaves you reeking of a feminine aroma (especially if you've had to wash your oiled hair)! It that rare situation, I've managed to get away with an excuse to run in to the shower as soon as I get home, quickly disguising my girly stink with some solid manly Lynx!