Bloodless surgery
Vincent Price removes the Tingler from Ollie's wife apparently by reaching through her skin and grabbing it. There is no blood gushing from the necessary gaping hole; Ollie just carries her out in a sheet.
And later, the doctor just grabs the Tingler and reinserts it in the wife. Again, no blood, no stitches.
Well, I guess it makes as much sense as the rest of the movie.