I assume the boxes are moved over an conveyor belt of somse sort.
Is the tape parallel to the conveyor belt, or square to it (What's the word?)
I would not rely on a single sensor, but would do at least 2 measurements and compare those.
One measures a base level of reflection on an area there should not be tape, and another measurement which measures the reflection level of the tape.
If the tape is longitudinal (parallel) to the conveyor belt this would need 2 sensors, but if the tape is at a 90degree angle to the conveyor belt, you can measure refelctivity of both and even measure the width of the tape (assume constant speed of the belt ?)
So if you have your sensor output "change" for a time comparable with the widht of the tape, you have a big chance it's really tape you have just measured.
Also, stuff like reflectivity & transparancy is wavelength dependent. Some time ago I saw a few pictures made with an IR camara of a sowing machine, which had a black rubber timingbelt in it. On the IR photograph, the rubber of the timing belt was almost invisible. You could see right through it, but the strengthening wires in the timingbelt were pitch black.
You could make something with fast blinking laser pointer and a photo diode in a tube.
The tube shields from most of the ambient light, and the blinking of the laser pointer (a few kHz) can also be used to distinguish from other light sources.
Some problems with this approach are with non-uniform color of the box (dirty patches, labels, etc)
A completely other approach is not to detect the tape itself, but the tape dispenser. Put some rotation sensor (encoder) on the roll of tape itself (or with a friction wheel, etc). If a box passes the tape dispenser, and no tape is dispenced, you have a box without tape.
More accurate: Measure the length of tape dispensed, so it also detects if a box is only half taped.