Recommendation for metal finding method
Pretty much all industrial/food metal detectors I've come across will easily detect the presence of metal foil tape in one diaper in a box of several diapers. It will probably register as a massive signal. I've designed them so I know how sensitive they are. For instance, a metal detector with an aperture of 14" x 7" can easily detect a 1 mm diameter piece of iron running through the centre of the aperture. On one application I remember, you could regularly detect the presence of iron naturally contained in a cabbage.

Finding a thin sheet of conductive tape will be a breeze.

They will also be able to stop the converyor (that you should feed them through) at a place indicative of the diaper that is containing the rogue material. Standard metal detectors like this have an output that can trip a belt motor or activate a reject arm. Pretty standard stuff.

I just don't think you've done your homework enough. Try looking up Apex metal detector (Thermo Scientific): -



The most basic search heads work with three coils like this: -



As the metal contaminate passes through the coils, there is a large "positive" signal followed by a sharp zero signal (metal in centre) followed by a large anti-phase (negative) signal. The positive and negative signals largely coincide with the positions of the outer receive coils and, because the geometry of those coils is known, it's a small matter to compute the (fairly) precise position of a rogue piece of metal and stop the conveyor at a fairly precise inspection point.