Have you tried contacting UA's lost and found in case it's not in the trash?
I empathize with you, but if I lost an item personally that I believed was in the trash, I would find gloves and do it myself rather than ask a police officer (not saying you didn't do this as I couldn't tell from your post, just trying to say that asking the police would have been a lost cause unless you had proof someone took it / stole it / a crime was committed). That's not their job.