All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
What this woman said is a mere claim, and she is required to prove it. If you do not believe her, then she is obliged to bring forth evidence to support her claim; otherwise, it is a worthless claim and you are not obliged to give her anything.
The relevant sharee'ah ruling states that the proof must be provided by the claimant and the oath (of denial) must be taken by the defendant who denies the claim. The Prophet, sallallaahu ʻalayhi wa sallam, said, “If people were given whatever they claimed (in disputes), then some people would claim the lives and wealth of others; but the proof is on the claimant and the oath is on the defendant.” Another version of the hadeeth reads, “...and an oath must be taken by the one who rejects the claim.” [Al-Bayhaqi and others] An-Nawawi stated in his book Al-Arbaʻeen An-Nawawiyyah that this is a hasan (good) hadeeth and that part of it was cited in Saheeh Al-Bukhari and Saheeh Muslim.
Hence, if this woman does not bring forth evidence to support her claim, then you should take an oath denying that you know anything about your mother's debt to her, and thus her claim is rejected and you are not obliged to repay her. For more benefit, please refer to fatwa 280108.
However, if she proved that your mother owed her the debt in reference, then you are obliged to repay it from your mother's estate before dividing it among the eligible heirs. Allaah, The Exalted, says (what means): {...after any bequest he (may have) made or debt...} [Quran 4:11] If you already divided the estate among the heirs, then you are obliged to take it (the debt) from the shares of the heirs and repay it without canceling the division of the estate. Ibn ʻAabideen wrote:
“If the heirs divided the estate and then discovered that the deceased was liable for a debt that consumes the whole estate or most of it, then the heirs are requested to repay it. If they repaid the debt, then the division of the estate is valid and acceptable; otherwise, it is declared null and void and must be canceled. This is because the settlement of debts is given precedence over the heirs' right to the estate. Hence, the heirs are not entitled to their shares unless they repay the debt or the creditor clears the deceased's liability from it. In this case, the division of the estate is valid since there is no lawful impediment. The same applies if the debt does not consume the whole estate; that is because the heirs are obliged to repay the rights of the creditors from the estate, unless the remainder of the estate after the division is enough to pay off the debt. In this case, there is no need to cancel the division given the absence of the need. The same is underlined in the chapter entitled 'division' in (the Hanafi book) Ad-Durar.” [Haashiyat Ibn ʻAabideen]
In case the debt claim was proven, then if the mother left behind enough wealth to pay off the debt, it must be paid off. But if she did not leave behind wealth to pay off the debt, then you are not obliged to repay her debt. It is recommended, though, to repay it out of dutifulness towards the mother.
Finally, it should be noted that the settlement of disputes, conflicts, and similar cases is the responsibility of the judicial authorities.
Allaah knows best.