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var array = ['A', 'B', 'C']; // Test
var search_term = 'B';

for (var i=array.length-1; i>=0; i--) {
    if (array[i] === search_term) {
        array.splice(i, 1);
        // break;       //<-- Uncomment  if only the first term has to be removed
    }
}