that deeds are reached up to heaven on these days and are the days of forgiveness
On Judaism, we read in Wikipedia:
Mondays and Thursdays are considered especially auspicious days for fasting. Traditionally, one also fasted upon awakening from an unexpected bad dream although this tradition is rarely kept nowadays.
The Polish Jews are accustomed to fast on the twentieth of Siwan on account of the atrocities committed on that day in 1648 by the Cossacks. Some pious Jews also fast every Monday and Thursday in commemoration of the destruction of the Temple, of the burning of the Torah, and of the desecration of God's name (comp. Luke xviii. 12).
It was customary to hold public fast days on Mondays and Thursdays (Tosef. to Ta'an. 2:4); individuals, however, especially after the destruction of the Temple, took upon themselves to fast every Monday and Thursday (Ta'an. 12a).
The first Monday and Thursday, and the following Monday after Passover and Sukkot (Tur and Sh. Ar., OḤ, 492). This fast was interpreted as an atonement for possible sins committed while in a state of drunkenness and gluttony during the holidays (see Tos. to Kid. 81a S.V. Sekava).
Reading of Torah on Mondays and Thursdays:
At first glance, this would seem to contradict the tradition3 that Ezra the Scribe and the Men of the Great Assembly introduced the practice of reading the Torah on Mondays and Thursdays in the 4th century BCE.... 2. The Tosafot (ad loc.) add that the choice of Monday and Thursday had additional significance to Moses since when he received the second set of Tablets he ascended Mount Sinai on the last Monday in Av and came down on Thursday, 10 Tishrei.
The Shulchan Aruch suggests that Monday and Thursday were picked to be the two days of fasting because these are Yemei Ratzon (days of grace). It points out that Moses went up a second time to Mount Sinai to receive the Torah on a Thursday and came down on a Monday.
Now let's see what Islam says:
It was narrated that ‘Aa’ishah (may Allaah be pleased with her) said: The Prophet (peace and blessings of Allaah be upon him) was keen to fast on Mondays and Thursdays. Narrated by al-Tirmidhi, 745; al-Nasaa’i, 2361; Ibn Maajah, 1739; classed as saheeh by al-Albaani in Saheeh al-Targheeb, 1044.
It was narrated from Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Deeds are shown (to Allaah) on Mondays and Thursdays, and I like my deeds to be shown when I am fasting.” Narrated by al-Tirmidhi, 747; classed as saheeh by al-Albaani in Saheeh al-Targheeb, 1041.
There is no doubt that fasting on Mondays and Thursdays is superior and that no other days could stand in their position, for the Prophet, sallallaahu ‘alayhi wa salam, favored them over other days by fasting on them. In justifying his fasting on them very often, he informed us that a person’s deeds are shown to Allaah The Almighty on these days, according to the narration by At-Tirmithi on the authority of Abu Qataadah may Allaah be pleased with him; and An-Nasaa'i on the authority of Usaamah.
Al-Tirmidhi Hadith 2055 Narrated by Aisha
Allah's Messenger (saws) used to fast on Mondays and Thursdays.
Related by Tirmidhi and Nasa'i.
Al-Tirmidhi Hadith 1261 Narrated by Abu Hurayrah
The Prophet (saws) said: ‘A man's deeds are presented (to Allah The Most Exalted) on Mondays and Thursdays and I prefer that I should be observing fast when my deeds are presented.’
Hadrat Abu Qatadah (r.a.) reported: ‘The Messenger of Allah (saws) was asked about fasting on Mondays. He (saws) said, "That is the day on which I was born and the day on which I received Revelation.``
Islam borrowed the custom of fasting on Mondays and Thursdays from the children of Israel because they are the days of Grace, Torah and forgiveness. These days mankind's deeds reach up to heaven and are judged. The Prophet Muhammed was born on a Monday and the final revelation came down on a Monday making it a favourable day for "fasting".