How to identify masked images of MODIS LAI 8Day product and drop the before downloading?

Question

I am trying to download set of MODIS LIA 8day products to my computer from Google Earth Engine. However, i have difficult time to drop masked images before downloading. Basically my code is taking set of aoi geometry from a file and then it build image collection and mask before create download url for every image in the collection.

# time window
start_dt = '2000-05-01'
end_dt   = '2023-12-31'

# cloud mask for MODIS LAI
def build_cloud_mask(image):
    # select the qc band
    qc_lai = image.select(['FparLai_QC'])
    # Define cloud bits (3-4 and 01 and 10)
    cloud_bits =     qc_lai.bitwiseAnd(0b00011000).rightShift(3).add(qc_lai.bitwiseAnd(0b00000011).rightShift(0))
    # mask
    cloud_mask = cloud_bits.eq(1).Or(cloud_bits.eq(2))
    # Apply the mask to the image
    return image.updateMask(cloud_mask.Not())


for index, row in ads_sample.iterrows():
    # Extract corner coordinates
    corners = list(row['geometry'].exterior.coords)
    new_polygon = Polygon(corners)

    # create ee geometry
    #aoi  = ee.Geometry.Polygon(new_polygon)
    aoi  = ee.Geometry.Polygon([list(coord) for coord in corners])
    modis_collection = ee.ImageCollection("MODIS/061/MOD15A2H").filterBounds(aoi).filterDate(start_dt, end_dt)
    # summer collection
    summer_collection = modis_collection.filter(ee.Filter.calendarRange(6, 7, 'month'))
    # masking the collection
    modis_lai_masked = summer_collection.map(build_cloud_mask)
    # filter images with any clouds
    # images to a list
    image_list = modis_lai_masked .toList(modis_lai_masked .size())
    # take image list and gothrough each of them for download

    # create folder for images
    ads_id = row['id']
    folder_path  = './output/images/'+str(ads_id)
    print(folder_path)
    # create folders
    try:
        os.makedirs(folder_path)
    except:
        print('Folder in place already')
    # number of images in collection for aoi
    num_images = modis_lai_masked.size().getInfo()
    for item in range(0, num_images):
        # take images
        filter_image = ee.Image(image_list.get(item))
        # take band
        filter_band = filter_image.select(['Lai_500m', 'FparLai_QC'])
        # clip to aoi
        filter_band = filter_band.clip(aoi).unmask()
        # image name
        im_name = str(filter_band.get('system:index').getInfo())
        #print(im_name)
        # take url
        try:
            url = filter_band.getDownloadURL({'scale':500,
                                                    'filePerBand':False, 
                                                    'region':aoi,
                                                    'crs':'EPSG:26911', 
                                                    'maxPixels': 1e13})
            print(url)
            

I tried counting number of masked images, but it turns to be all images are cloudy, which is not true for these set of images.