Do you compost freezer boxes with wet strength?

So, here's a hypothetical for you. Let's just say you're an EnviroMom who's had a really, really long and trying week. Generally, you avoid convenience foods like the plague. But in a moment of weakness, when you just happened to be really, really close to Trader Joe's, you popped in with the plan of getting a baked good or two for a preschool open house. And since hypothetical EnviroMom happened to be shopping without her two appendages (translation: children) she actually had some quiet, enjoyable moments to peruse the aisles, where it suddenly occurred to her that the only thing for dinner was a few leftovers, which are often a hard-sell. So in a moment of weakness, this hypothetical EnviroMom bought a frozen pizza. I swear, it's never happened before.

What a long set-up to one discussion question, huh? Keep with me. So here's my question. Do you put freezer boxes, such as those from frozen pizzas or frozen waffles into your compost? It's clear to me that you never, never put them in curbside paper recycling. But it sure does seem sacrilegious to just throw them away. My understanding of wet-strength injected papers is scant at best. I do understand that the goal of composting is to add good things to the soil, and that food-contaminated napkins, newsprint, cardboard, etc. can fall under the list of "good things." But does that extend to cardboard that has wet strength?

What do you do? Do you add cardboard with wet strength to your home compost? Any advice for the hypothetical EnviroMom, just trying to do the right thing?