Today's Dilbert made me laugh but I found the second panel ungrammatical.
The antecedant of the plural "them" is the singular "every part of your body".
Secondly, when I checked with my sister Jenni she pointed out the use of "would" in that panel doesn't sound right either. It implies the existence of the procedure is hypothetical, which is not how it is presented in the first panel.
The "would" might just be a difference between Australian English and American English but it could also be a subtle slip up because the procedure is, in fact, hypothetical.
The "them" is, however, just plain ungrammatical as far as I can tell.