This is the most authentic Tafsir, by Ibn Kathir.
There is no Sin on Elderly Women if They do not wear a Cloak
[RIGHT]وَالْقَوَاعِدُ مِنَ النِّسَآءِ][/RIGHT]
(And the Qawaid among women.) Said bin Jubayr, Muqatil bin Hayyan, Ad-Dahhak and Qatadah said that these are the women who no longer think that they can bear children,
[RIGHT]الَّلَـتِى لاَ يَرْجُونَ نِكَاحاً][/RIGHT]
(who do not hope for marriage,) meaning, they no longer have any desire for marriage,
[RIGHT]فَلَيْسَ عَلَيْهِنَّ جُنَاحٌ أَن يَضَعْنَ ثِيَابَهُنَّ غَيْرَ مُتَبَرِّجَـتِ بِزِينَةٍ][/RIGHT]
(it is no sin on them if they discard their (outer) clothing in such a way as not to show their adornment.) meaning, they do not have to cover themselves in the same way that other women have to. Abu Dawud recorded that Ibn `Abbas said that the Ayah:
[RIGHT]وَقُل لِّلْمُؤْمِنَـتِ يَغْضُضْنَ مِنْ أَبْصَـرِهِنَّ][/RIGHT]
(And tell the believing women to lower their gaze) [24:31] was abrogated and an exception was made in the case of:
[RIGHT]وَالْقَوَاعِدُ مِنَ النِّسَآءِ الَّلَـتِى لاَ يَرْجُونَ نِكَاحاً][/RIGHT]
(the past childbearing among women who do not hope for marriage, .)
[RIGHT]فَلَيْسَ عَلَيْهِنَّ جُنَاحٌ أَن يَضَعْنَ ثِيَابَهُنَّ][/RIGHT]
(it is no sin on them if they discard their (outer) clothing) Ibn Masud said about (outer) clothing,, "The Jilbab or Rida'.'' A similar view was also narrated from IbnAbbas, Ibn Umar, Mujahid, Said bin Jubayr, Abu Ash-Shatha', Ibrahim An-Nakhai, Al-Hasan, Qatadah, Az-Zuhri, Al-Awzai and others.
[RIGHT]غَيْرَ مُتَبَرِّجَـتِ بِزِينَةٍ][/RIGHT]
(in such a way as not to show their adornment.) Sa`id bin Jubayr said, "They should not make a wanton display of themselves by removing their outer garment so that their adornment may be seen.''
[RIGHT]وَأَن يَسْتَعْفِفْنَ خَيْرٌ لَّهُنَّ][/RIGHT]
(But to refrain is better for them.) means, not removing their outer garment, even though that is permissible for them, is better for them.
[RIGHT]وَاللَّهُ سَمِيعٌ عَلِيمٌ][/RIGHT]
(And Allah is All-Hearer, All-Knower.)