The Quran

يا أَيُّهَا الَّذينَ آمَنوا إِذا جاءَكُمُ المُؤمِناتُ مُهاجِراتٍ فَامتَحِنوهُنَّ ۖ اللَّهُ أَعلَمُ بِإيمانِهِنَّ ۖ فَإِن عَلِمتُموهُنَّ مُؤمِناتٍ فَلا تَرجِعوهُنَّ إِلَى الكُفّارِ ۖ لا هُنَّ حِلٌّ لَهُم وَلا هُم يَحِلّونَ لَهُنَّ ۖ وَآتوهُم ما أَنفَقوا ۚ وَلا جُناحَ عَلَيكُم أَن تَنكِحوهُنَّ إِذا آتَيتُموهُنَّ أُجورَهُنَّ ۚ وَلا تُمسِكوا بِعِصَمِ الكَوافِرِ وَاسأَلوا ما أَنفَقتُم وَليَسأَلوا ما أَنفَقوا ۚ ذٰلِكُم حُكمُ اللَّهِ ۖ يَحكُمُ بَينَكُم ۚ وَاللَّهُ عَليمٌ حَكيمٌ

Muhammad Asad

O YOU who have attained to faith! Whenever believing women come unto you, forsaking the domain of evil,¹ examine them, [although only] God is fully aware of their faith;² and if you have thus ascertained that they are believers, do not send them back to the deniers of the truth, [since] they are [no longer] lawful to their erstwhile husbands,³ and these are [no longer] lawful to them. None the less, you shall return to them whatever they have spent [on their wives by way of dower];⁴ and [then, O believers,] you will be committing no sin if you marry them after giving them their dowers. On the other hand, hold not to the marriage-tie with women who [continue to] deny the truth,⁵ and ask but for [the return of] whatever you have spent [by way of dower] - just as they [whose wives have gone over to you] have the right to demand⁶ [the return of] whatever they have spent. Such is God's judgment: He judges between you [in equity] - for God is all-knowing, wise.

Lit., "as emigrants" (muhajirat). For an explanation of my rendering this term as above, see surah 2, note 203.
Under the terms of the Truce of Hudaybiyyah, concluded in the year 6 H. between the Prophet and the pagan Quraysh of Mecca, any Meccan minor or other person under guardianship who went over to the Muslims without the permission of his or her guardian was to be returned to the Quraysh (see introductory note to surah 48). The Quraysh took this stipulation to include also married women, whom they considered to be under the "guardianship" of their husbands. Accordingly, when several Meccan women embraced Islam against the will of their husbands and fled to Medina, the Quraysh demanded their forcible return to Mecca. This the Prophet refused on the grounds that married women did not fall within the category of "persons under guardianship". However, since there was always the possibility that some of these women had gone over to the Muslims not for reasons of faith but out of purely worldly considerations, the believers were enjoined to make sure of their sincerity; and so, the Prophet asked each of them: "Swear before God that thou didst not leave because of hatred of thy husband, or out of desire to go to another country, or in the hope of attaining to worldly advantages: swear before God that thou didst not leave for any reason save the love of God and His Apostle" (Tabari). Since God alone knows what is in the heart of a human being, a positive response of the woman concerned was to be regarded as the only humanly attainable - and, therefore, legally sufficient - proof of her sincerity. The fact that God alone is really aware of what is in a human being's heart is incorporated in the shar'i principle that any adult person's declaration of faith, in the absence of any evidence to the contrary, makes it mandatory upon the community to accept that person - whether man or woman - as a Muslim on the basis of this declaration alone.
Lit., "to them". Thus, if a wife embraces Islam while her husband remains outside its pale, the marriage is considered, from the Islamic point of view, to have been automatically annulled.
Such an annulment is to be subject to the same conditions as a khul' (dissolution of marriage, at the wife's instance, from her Muslim husband - see note 218 on the second paragraph of 2:229): that is to say, since the non-Muslim former husband is presumed to have been innocent of any breach of his marital obligations as such, the wife is to be considered the contract-breaking party and has, therefore, to refund the dower (mahr) which she received from him at the time of concluding the marriage. In case of her inability to do so, the Muslim community is obliged to indemnify the erstwhile husband: hence the plural form in the imperative "'you shall return" (lit., "give").
I.e., such of the pagan wives of Muslim converts as refuse to abandon their beliefs and their non-Muslim environment, in which case the Muslim husband is to regard the marriage as null and void. As for Muslim wives who, abandoning their husbands, go over to the unbelievers and renounce their faith, see verse 11.
Lit., "and let them demand...", etc.