If you mean the bit of noise right at the start of the track, that's actually not a finger on strings, that's vinyl noise. It was much more noticable when played on the old turntable. I did a "fade-in" on it to make it even less noticable.
I've wondered if that was also a different performance than on BHOE - and not just strings and piano thrown on top over the LP track... it sounds like the vocals are just slightly different to me.
Here's a photo of the 45:
Oh, about that MFSL Sundown - one of my copies is the official release, by my other copy, that's a blank-label test pressing.