None of the scholars – as far as we know – stated that women should wash menstrual pads on which there is some blood before throwing them away. Rather it seems that the Sahaabiyaat did not wash these rags, and the Prophet (peace and blessings of Allaah be upon him) knew of that but there is no report that he told them not to do that. Al-Tirmidhi (64) narrated that Abu Sa’eed al-Khudri (may Allaah be pleased with him) said: It was said: O Messenger of Allaah, should we do wudoo’ from Bi’r Budaa’ah [a well]? It is a well in which menstrual rags, the flesh of dogs and rotten things are thrown. The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Water is a means of purification and nothing makes it impure.” It is a saheeh hadeeth; it was  classed as saheeh by Ahmad, Yahya ibn Ma’een, Ibn Khuzaymah, Ibn Taymiyah and others (may Allaah have mercy on them). 

It seems that they used to throw them away when they were stained with blood, otherwise the Sahaabah would not have asked about the purity of the water in which these rags were found. 

The hadeeth does not mean that they used to throw these things into the well deliberately, because the Sahaabah (may Allaah be pleased with them) were greater and better than that. Rather what is meant is that the well was in the bed of some wadi, and when the rain came the flood would carry these things and throw them in the well. 

And Allaah knows best.