Unless something has changed, I don't think the badge was insured and I don't believe it will be replaced for free.
Personally, I would just send EO an email tonight and ask them what the policy is since they will know and it's quite probable your officers won't off the top of their heads. You'll probably get an answer first thing in the morning when everyone gets to EO.
So sorry this happened to you! Saying a little prayer it will show up!