Once you've done one tab, and cleared the opening... do the next tab!
The sheath will now slide a little more than it did before. To fully release it, you'll need to take care of the main retention mechanism that keeps the module in the parent equipment's cage. Depress the triangle, and slide the sheath further.
This final clip is actuated by the main release handle, but that doesn't generally get it far enough out of the way to remove the sheath (only remove the module from the cage).
The final hurdle is probably the label... I've taken apart some modules where the label is not an issue, and others (like this one - oopsy), where the label interferes and gets scuffed.
A screwdriver can be inserted under the EMI fingers to just lift the sheath slightly away from the label.