Perhaps you can compress the tar file using the “gzip.GzipFile” class. It accepts a custom “mtime” parameter (see Issue 4272, added in 2.7 and 3.1+):

>>> gztar = BytesIO()
>>> tar = GzipFile(fileobj=gztar, mode="w", mtime=0)
>>> tarfile.open(fileobj=tar, mode="w|").close()
>>> tar.close()
>>> gztar.getvalue().hex()
'1f8b08000000000002ffedc1010d000000c2a0f74f6d0e37a00000000000000000008037039ade1d2700280000'

However, “tarfile.open” accepts a “compresslevel” argument for two of the compressors, so you could argue it is okay to add another argument to pass to the gzip compressor.