I was at Pop a couple of weeks ago and couldn't believe they were putting the food on a tray. I ordered after returning from Epcot in the middle of a thunderstorm/monsoon. When I asked for a bag so I could take my food back to my room, I was told they didn't have any bags. When I asked the CM how I was supposed to carry a tray of food in pouring down rain, she reluctantly gave me a very small bag and said that was all they had. I had only ordered fries and a tie dye cheesecake, so luckily it fit.
I suppose they are using trays now since it's cheaper than using the brown paper bags with handles that they had in August. Interestingly, I went to the QS at Riviera Resort the next day and they had an abundance of those paper bags that have disappeared from Pop.
My suggestion is to bring some plastic bags with you or perhaps repurpose a merchandise bag or a reusable bag for transporting your food if you plan to eat in your room. I would also recommend bringing some paper plates as it is not easy to eat out of those little cardboard boxes.
I also have to say that I was pretty disappointed in the quality of the food at Pop. I used to love it, but other than the cheesecake, I didn't have anything that I actually liked.
If the skyliner is running, I highly recommend getting food from Primo Piatto or Bar Riva at Riviera Resort. If you have a car, go offsite for food. I found a Panera and a Chick fil a within a couple of miles.