Usually you can silence an alarm by reinserting the key in any door or trunk lock and turn from unlock to lock then back to unlock.
Probably what happened in your case was the key was not turned far enough to disengage the alarm or it was turned too fast. Also I agree with the prior poster that it would be smart to remove it if its aftermarket.

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81 300CD (sold) 1972 280 SEL 4.5 (sold) 1966 250 S 4 spd (sold) 1974 450 SL (sold) 86 BMW 325ES (sold), 1973 280C (sold) 1988 300 SE.