In the gospel accounts, the woman who is linked to the washing of Jesus’ feet is described in Matthew, Mark, and Luke as a woman who enters the house, breaks open the alabaster jar, and washes Jesus’ feet. Here are those accounts:
Mat 26:6-13 KJV - 6 Now when Jesus was in Bethany, in the house of Simon the leper, 7 There came unto him a woman having an alabaster box of very precious ointment, and poured it on his head, as he sat at meat. 8 But when his disciples saw it, they had indignation, saying, To what purpose is this waste? 9 For this ointment might have been sold for much, and given to the poor. 10 When Jesus understood it, he said unto them, Why trouble ye the woman? for she hath wrought a good work upon me.
Mar 14:3-9 KJV - 3 And being in Bethany in the house of Simon the leper, as he sat at meat, there came a woman having an alabaster box of ointment of spikenard very precious; and she brake the box, and poured it on his head. 4 And there were some that had indignation within themselves, and said, Why was this waste of the ointment made? 5 For it might have been sold for more than three hundred pence, and have been given to the poor. And they murmured against her. 6 And Jesus said, Let her alone; why trouble ye her? she hath wrought a good work on me.
Luk 7:36-50 KJV - 36 And one of the Pharisees desired him that he would eat with him. And he went into the Pharisee's house, and sat down to meat. 37 And, behold, a woman in the city, which was a sinner, when she knew that Jesus sat at meat in the Pharisee's house, brought an alabaster box of ointment, 38 And stood at his feet behind him weeping, and began to wash his feet with tears, and did wipe them with the hairs of her head, and kissed his feet, and anointed them with the ointment.
These accounts are known as the synoptic gospels because these three gospels are very similar in their accounts of the life of Jesus. Scholars have suggested that the reason these accounts are so similar is because they copied off each other (see the illustration below). Mark, it is believed, was the first gospel and was a collection of sermon by Peter (remember that Mark was not a direct disciple of Jesus, but a disciple of Peter). Mark’s gospel was followed by Matthew- written by the apostle Matthew, followed by Luke (also not a direct disciple of Jesus), who also wrote the book of Acts. In each case, the writer added a little more to the story of Jesus first recorded by Mark.
But the gospel of John is not synoptic to the other three gospels, and as a result the account is slightly different. Here is that account:
Jhn 12:1-11 KJV - 1 Then Jesus six days before the passover came to Bethany, where Lazarus was which had been dead, whom he raised from the dead. 2 There they made him a supper; and Martha served: but Lazarus was one of them that sat at the table with him. 3 Then took Mary a pound of ointment of spikenard, very costly, and anointed the feet of Jesus, and wiped his feet with her hair: and the house was filled with the odor of the ointment.
So why the different accounts on the washing of Jesus’ feet? There may be a few reasons:
#1- There are two different incidents. One in which Mary anoints the feet of Jesus and one in which a stranger anoints the feet of Jesus. One incident occurs in Martha’s house and one in Simon the Leper’s house
#2- The name and the place of the anointed got lost in the oral tradition of the synoptic gospels, while John’s account retained the information
#3- The name and place was not retained in John’s account, but was retained in the synoptic gospel
#4- The incident occurs in Bethany, at the house of Simon the Leper, who may have been related to Lazarus, and who may have been a pharisee (remember that the pharisees are a sect of Judaism- and wildly popular in Jesus’ day). Or it may have taken place at the house of Martha, who was closely linked to Simon her relative. (We do not know, but they may have even lived in close proximity to each other, or even with each other). Mary is the woman who did the foot washing, and the synoptic gospels may have left her name out to protect her identity, or her name was simply lost over time. John chose not to exclude her name.
In my opinion #4 seems the most likely answer for a few reasons: 1) the people involved are the in all four accounts because they are probably related to each other 2) Mary is always pictured in Scripture as a very devoted follower of Christ, and 3) We often see Mary pictured at the feet of Jesus.
In all these cases where Scripture appears to be different between the gospels, always look for the similarities and explore the historicity before drawing your conclusions.