At least one woman anointed Jesus

Matthew 26:

When Jesus had finished saying all these things, he said to his disciples, ² “You know that after two days the Passover is coming, and the Son of Man will be handed over to be crucified.”

³ Then the chief priests and the elders of the people gathered in the palace of the high priest, who was called Caiaphas, ⁴ and they conspired to arrest Jesus by stealth and kill him. ⁵ But they said, “Not during the festival, or there may be a riot among the people.”

Mark and Luke don't name Caiaphas among the conspirators. Josephus said that Caiaphas was appointed by the Roman prefect who preceded Pilate.  John does name him, but has a different perspective on their motives, claiming that the conspiracy was a response to the raising of Lazarus, a miracle the other gospel writers never mention. Death and Raising of Lazarus

I have avoided going over all the differences among the four gospels to focus on what Matthew is saying, but certain stories appear in all of them, and a story of a woman anointing Jesus is one of them. Matthew follows Mark's account, placing the incident in Bethany, the home of Simon the Leper, and right after the chief priests' conspiracy and before Judas' betrayal. Neither of them give the woman's name.

⁶ Now while Jesus was at Bethany in the house of Simon the leper, ⁷ a woman came to him with an alabaster jar of very costly ointment, and she poured it on his head as he sat at the table. ⁸ But when the disciples saw it, they were angry and said, "Why this waste? ⁹ For this ointment could have been sold for a large sum, and the money given to the poor." ¹⁰ But Jesus, aware of this, said to them, "Why do you trouble the woman? She has performed a good service for me. ¹¹ For you always have the poor with you, but you will not always have me. ¹² By pouring this ointment on my body she has prepared me for burial.¹³ Truly I tell you, wherever this good news is proclaimed in the whole world, what she has done will be told in remembrance of her."

¹⁴ Then one of the twelve, who was called Judas Iscariot, went to the chief priests ¹⁵ and said, “What will you give me if I betray him to you?” They paid him thirty pieces of silver. ¹⁶ And from that moment he began to look for an opportunity to betray him.

John names Judas as the disciple to complain about the waste of money, and also accuses Judas of stealing from the funds. Matthew and Mark give the impression that Judas may have been motivated by the incident of the anointing, but don't say so explicitly. John also names the woman ( who anoints Jesus' feet) as Mary, sister of Martha and Lazarus.
John's version of the anointing 

Although Luke, like Matthew, follows Mark's account of these last days, he doesn't have the story of the anointing here. Instead, his story takes place about as far from the passion narrative as it could be, earlier in Jesus' ministry in Capernaum. It could be a different episode, except for the coincidence that the host is, as in Mark and Matthew, named Simon ("the Pharisee"  instead of "the Leper"). Also, like John's story, Luke says the woman anointed Jesus' feet and wiped them with her hair. Mark and Matthew only say she poured oil on his head. Luke doesn't name her, but he has a different story about two sisters named Mary and Martha, with no mention of a brother Lazarus.
Luke's story about Mary and Martha

I'm not going to try to harmonize these four accounts. There is no reason in the text to believe that this Mary was Mary Magdalene, as some traditions hold, but at this point you can see why there would be confusion.