That clip is not your problem. With that clip missing all that will happen is the pads will flap upon the rotor while the
brakes are not activated.
What you are saying is different:
brakes chatter when rear brake is used
Reasons for this could be several but I would suspect it is the results of the brake job itself. Maybe you got brake fluid on the brake pads!
Some air in the line may be causing the chatter, it's happened before so I would also suggest to bleed the brake lines.
An out of alignment caliper may cause the brakes to chatter.
Continuing to use the brakes may straighten out whatever is causing the problem and I would give that a chance to happen also. More like seat the pads in.
But I'd be sure to bleed the brakes first.
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