Is it really necessary to cleanse a new tarot deck?

The deck I recently purchased was an Atlantis deck and was pre-owned (although never used). I did a couple of readings for myself which, now upon thinking about it, gave quite confusing outcomes. Should I have cleansed the deck before smudging it?

In the process of smudging I made up a sigil and burned it in the traditional Chaos Magick manner (an oxymoronic statement if ever there was one), i used the smoke form the sigil to smudge the cards.

I'm now thinking that I should have performed a proper cleansing and put the deck under my pillow to make sure it was clean.

Any advice?