It is not permissible for a man to be alone with a non-mahram woman, because of the report narrated by al-Bukhaari (3006) and Muslim (1341) from Ibn ‘Abbaas (may Allaah be pleased with him), that he heard the Prophet (peace and blessings of Allaah be upon him) say: “No man should be alone with a woman without there being a mahram present, and no woman should travel unless she has a mahram with her.” A man stood up and said: O Messenger of Allaah, my wife has set out for Hajj and I have enlisted for such and such a campaign. He said: “Go and do Hajj with your wife.”
The fact that the Prophet (peace and blessings of Allaah be upon him) said “man” is general in meaning and applies to every man, even if he is elderly.
It says in al-Mawsoo’ah al-Fiqhiyyah (29/295): The majority of fuqaha’ say that it is not permissible for a man to be alone with a non-mahram woman, because the shaytaan will be the third one present, and he will whisper to them when they are alone together to do that which is not permissible. The Prophet (peace and blessings of Allaah be upon him) said: “No man is alone with a woman but the shaytaan is the third one present.” The word “man” in this hadeeth includes both old and young men, just as the word “woman” includes both young and old women. End quote.
If your grandfather needs someone to serve him because he is old, he can choose whichever of the following options suits him best, so that he will not be alone with a woman in the way that is haraam:
1- He could marry this woman who is serving him, or another woman, so that her staying in the house with him will not involve anything that goes against sharee’ah. The scholars (may Allaah have mercy on them) said that one of the purposes of marriage is to serve the husband, as in the case of your grandfather. See al-Sharh al-Mumti’ (10/383).
2- One of his children or grandchildren could serve him, so that he will have no need of this woman’s services.
3- If none of his children can serve him, then at least one of them could be present in the house at the times when the female servant is present, so that he will not be alone with her.
4- If that is not possible either, he can agree with the servant that she will come at a certain time, and he can go out of the house at that time, to buy whatever he needs, or to go and pray in the mosque and stay there for a while, or visit a friend or relative, and so on.
All of these are means of avoiding that which Allaah has forbidden.
We ask Allaah to help him to do that which is good and to protect him from sin.
And Allaah knows best.