var collection = ee.ImageCollection('NCEP_RE/surface_temp');
var AST2015 = collection.filterDate('2015-01-01', '2016-01-01');

var start_bad_data = '2015-06-18T00:00:00';
var end_bad_data = '2015-06-20T00:00:00';
var bad_data_filter = ee.Filter.date(start_bad_data, end_bad_data);

// Select the bad data.
var AST2015_bad_data = AST2015.filter(bad_data_filter);
// Select the good data.
var AST2015_good_data = AST2015.filter(bad_data_filter.not());

Map.addLayer(AST2015, {}, 'AST2015');
Map.addLayer(AST2015_bad_data, {}, 'AST2015_bad_data');
Map.addLayer(AST2015_good_data, {}, 'AST2015_good_data');