The main reason of the shield on the SSD is not protecting the SSD itself (although due to the principle of reciprocity, the computer and SSD are indeed also protected from the external interference), but to ensure that radiation from the computer conforms to electromagnetic compatibility regulations and does not generate harmful interference. You can say it's to protect the rest of the world from the computer and SSD. To protect the radio spectrum - a public resource shared by everyone - from mass-produced electronics, there are strict regulations on unintentional radiation from 30 MHz to 1 GHz and beyond. Before a new electronics gadget enters production, it's rigorously tested in a shielded anechoic chamber with a broadband antenna, the entire radio spectrum is scanned and checked to ensure that there are no spurious peaks.
Shielding is the primary method to comply with the regulations. Theoretically, the shield should completely enclosed the device by 360 degrees. But real devices have plugs, ports, slots, drive bays, and the shielding cannot be perfect. Sometimes these leaks have little effect, other times it can make the device to fail the regulatory compliance test - the effect is not obvious, and often can only be discovered by lab measurement. When a leak is found, additional shielding is strategically added to bridge the gap by the use of EMI foams, gasket, conductive tapes, metal enclosures, grounding screws, until the compliance test is passed.
Any aftermarket modification technically makes the computer uncertified as a whole. The end result may or may not comply with the regulations. However, since the purpose of these regulations is targeting mass-produced electronics, these kind of personal modifications are tolerated. Similarly, a self-built PC does not need to pass EMI/EMC compliance test for the same reason.
For personal use, a one-off modification like yours is usually a non-issue unless it's operating under unusual circumstances. Since the effect of shielding is often not obvious and counter-intuitive, even if one wants to restore its shielding, as an individual, one would not have access to a proper EMI test chamber to evaluate its effectiveness anyway. So as a personal user, the suggestion is just to "live with it" - it won't be less stable than any other self-built PC.