After the calf, Moses pitched his personal tent far from the people. Targum Pseudo-Jonathan, the Aramaic paraphrase of the Torah, gives us the exact distance and what happened there.
"He spread it without the camp, and removed it from the camp of the people to the distance of two thousand cubits; and it was called the Mashkan Beit Ulpana, the Tabernacle of the House of Instruction. When any one turned by repentance with a true heart before the Lord, he went forth to the Tabernacle that was without the camp, to confess and pray for the pardon of his sins; and praying he was forgiven" (Exodus 33:7).
Two thousand cubits. That is precisely the techum Shabbat, the Sabbath limit, the distance a Jew is permitted to walk outside a settled area on the day of rest. The Targum is planting the first seed of a rabbinic institution that will not be formalized for another fifteen hundred years.
The tabernacle served two functions. It was a beit midrash, a house of instruction where Moses taught Torah. It was also a beit teshuvah, a house of repentance. Whoever felt the mark of the calf still on him, whoever wanted to come back, walked out of the camp to this tent. They confessed. They prayed. They were forgiven.
Forgiveness required movement. You had to get up. You had to walk the two thousand cubits. You had to leave the camp of comfort and step toward the tent of learning.
Takeaway: Repentance in Jewish thought is not a feeling. It is a walk. Two thousand cubits in the right direction, and the gates of forgiveness open.