That metal sleeve goes inside the rubber bushing at the bottom of the shock. The bolt that holds the shock on the control arm will then pass through the metal sleeve. It’s necessary to prevent the shock from being loose since the hole in the rubber is much larger than the diameter of the bolt and to increase the life of the rubber bushing. See the green arrow I added to your picture. You really should install them.

As to your bouncy issue. My opinion is the shocks you bought are just low quality. I have seen many threads over the years about poor ride quality after installing Gabriel brand shocks. Return them and get KYBs, Bistiens, or even ranchos if you want a smoother ride.

 

As to your bouncy issue. My opinion is the shocks you bought are just low quality. I have seen many threads over the years about poor ride quality after installing Gabriel brand shocks. Return them and get KYBs, Bistiens, or even ranchos if you want a smoother ride.

Agree the Gabriels are junk. I am a big fan of the KYB Gas-A-Just if you really want a stiff, sporty ride

 

I dunno, the Gabriel's I have on mine are great. I have the G63813's. They have a very large diameter housing.

 

shocks vary, some are made to ride softer, some firmer. they prolly have various types. of course if that sleeve is not in + bolts are loose shocks won't function properly