Sorry to hear about your negative. I agree with Digital*Ghost that if you detach the socks from the original packaging it doesn't matter that you include it with the socks, the item becomes "New Without Tags". 

Based on my personal experience, if I was a Buyer, I'd assume that you had a vacuum press packing machine and simply put - use it for flat packaging, but not detaching from the original setting because your pictures show intact products.

I bought a few items before, Sellers advised in their listings that items are flat packed for shipping. The items did come flat packed but opposing to your hand repackaging they were in the original setting, because they used this vacuum press packing machine. The downside of this type of packaging was that the items came out from the pack with deep wrinkles and I had to steam iron them (if not washing first)  to get to the original condition. Not good for gift giving.