New Defender's Study Bible Notes
7:37 a sinner. Probably this implies she had been a prostitute, and many have assumed it was Mary Magdalene. This is unlikely, however, for Luke does not identify her, whereas Mary Magdalene is clearly identified just a few verses further on (Luke 8:2), and apparently was a woman of some substance (Luke 8:3).
7:37 alabaster box of ointment. This event took place in Galilee, fairly early in Jesus’ ministry. Some time later, during the last days of His ministry on earth, Mary of Bethany (near Jerusalem), a devoted follower of Jesus, performed a similar act of devotion (John 12:3). It may well be that Mary had heard of the earlier act by the formerly sinful woman, and felt that she should do the same. See also note on Matthew 26:12.