Contact Invicta to see if they will get you one. In the meantime, go look for the filler piece, it's laying right where you won't look.
That's exactly how it works, if you won't look there, that is where it is. Use a flashlight laying on the floor and turn the beam illuminating everything that sticks up. Much easier to see it.
BTW you just learned why watch repair desks are high backed on three sides - to knock down and contain flying parts. If you are working on Mrs. Rumplebutz's old Rolex you cannot afford to lose a part long out of production. No different for you or me. Always work on watches in a corner of the room if at all possible, never on carpeting, and if you need to, inside a cardboard box propped up to catch flying bits.
You can still wear the watch without the lug hider, agreed that's a 'meh' idea. Switch to mesh and they don't have them. Nato or Perlon is another choice, in summer its a nice change. Invicta bracelets are out in the used market, too and somebody might have the fillers for sale in a watch forum.
The real problem is that now, you aren't happy with the watch and you might think it's time to try something else. Resist that impulse as much as possible, it leads to owning another - and you will then discover you're affect by Timepiece Associated Repair Dissonance Syndrome. Don't wake up next month to find you are now just like the rest of us TARDS, more watches than you can wear, no winder, and looking at G Shocks.