You can remove images of a collection by constructing a filter that selects the images you want to remove, then negatingnegate the filter using ee.Filter.not().
var MAX_LIST_SIZE = 100;
var collectionLS7NDVI0 = ee.ImageCollection('LANDSAT/LE7_L1T_32DAY_NDVI')
.filter(ee.Filter.calendarRange(6,6,'month'));
print('listOfImages', collectionLS7NDVI0.toList(MAX_LIST_SIZE));
// Filter out image(s) from 2005.
var filtered = collectionLS7NDVI0.filter(
ee.Filter.date('2005', '2006').not()
);
print('filtered', filtered.toList(MAX_LIST_SIZE));