“came into Jerusalem.” The exact meaning of “came into” (erchomai eis) must be determined from the context because it is used for “come to,” “come into,” “arrive at,” etc. In this case, Jerusalem was a walled city, so they literally “came into” it. They did not just “come to” it. Although the eastern wall of the Temple was part of the outer wall of Jerusalem, the main entrances to the Temple were from inside Jerusalem, especially from the south (which had both a double and triple entry gate) and from the west.
“doves.” The people who were poor and could not afford to bring or buy a lamb or goat were allowed to sacrifice doves, which were much less expensive (Lev. 12:8). Before the Magi came and gave gifts to Joseph and Mary, they were poor and had to sacrifice doves (Luke 2:24).