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That seems to be short organ part of the song.
KingBeeBuzz is Correct . There is no real outtakes of She Smiled Sweetly . The only thing that comes close is the Isolated Backing Track + Isolated Vocal Track i made from the regular stereo release for myself , because i enjoy making them and collecting them .
there are these in the 50YofDW folder 0.128 - 9-26 Nov 1966 (Olympic Sound Studios, London)
03 - She Smiled Sweetly (Mono, vinyl rip Decca LK 4852) 2:44
03 - She Smiled Sweetly (Stereo, Between The Buttons UK Version SACD) 2:47