Was the washing of feet of the disciples by Jesus, part of a Jewish tradition? At John 13:3-6 (RSVCE) we read: 


  Jesus, knowing that the Father had given all things into his hands, and that he had come from God and was going to God, rose from supper, laid aside his garments, and girded himself with a towel.  Then he poured water into a basin, and began to wash the disciples’ feet, and to wipe them with the towel with which he was girded.  He came to Simon Peter; and Peter said to him, “Lord, do you wash my feet?”


That the towel and the basin were already there, suggests that Jesus was enacting a traditional ritual of washing of the feet of the participants of  Passover feast, by the elder. The assumption is also corroborated by  the fact that only Simon Peter, who was not the first one to have his feet washed by Jesus, registered his objection.  

My question is: Are there any teachings from the side of Catholic Church confirming that Jesus was in deed reinforcing a Jewish tradition of washing the feet of one's  dear ones at Passover ?
On the contrary, the towel and basin were there for feet to be washed by themselves (Genesis 18:4 &amp; 19:2, Judges 19:21, 1st Samuel 25:41 and others). In that culture (and as an externality of wearing sandals), it was custom to have the feet of people who entered one's home washed. It had nothing to do with Passover specifically, but rather out of both respect and general desire for cleanliness. For example, look at the other known foot washing incident:


  Luke 7:37 And behold, a woman of the city, who was a sinner, when she
  learned that he was at table in the Pharisee's house, brought an
  alabaster flask of ointment, 38 and standing behind him at his feet,
  weeping, she began to wet his feet with her tears, and wiped them with
  the hair of her head, and kissed his feet, and anointed them with the
  ointment.


then later


  Luke 7:44 Then turning toward the woman he said to Simon, "Do you see
  this woman? I entered your house, you gave me no water for my
  feet, but she has wet my feet with her tears and wiped them with her
  hair.


Emphasis mine. It was a custom to have the things around for anyone entering the room - that a person entering the home would wash their own feet, or perhaps a servant would wash it for them. In addition, in Luke's account of passage at hand, you'll notice a different reason for Jesus getting his wash on, emphasis mine: 


  Luke 22:24 A dispute also arose among them, which of them was to be
  regarded as the greatest. 25 And he said to them, "The kings of the
  Gentiles exercise lordship over them; and those in authority over them
  are called benefactors. 26 But not so with you; rather let the
  greatest among you become as the youngest, and the leader as one who
  serves. 27 For which is the greater, one who sits at table, or one who
  serves? Is it not the one who sits at table? But I am among you as one
  who serves.


While the disciples jockey for whomever is the best, Jesus lowers and humbles himself, stripping down like a servant to wash those same disciple's feet. John records this dialogue as well, emphasis mine:


  John 13:12 When he had washed their feet, and taken his garments, and resumed
  his place, he said to them, "Do you know what I have done to you? 13
  You call me Teacher and Lord; and you are right, for so I am. 14 If I
  then, your Lord and Teacher, have washed your feet, you also ought to
  wash one another's feet. 15 For I have given you an example, that you
  also should do as I have done to you. 16 Truly, truly, I say to you,
  a servant is not greater than his master; nor is he who is sent
  greater than he who sent him.


There was no tradition here, until this point. This actually starts a Christian tradition, a sense of inward and outward humility. Paul's letter 1st Timothy 5:10 included "washed the feet of the saints" in instructions for the selection of widows who wish to be provided by the church. Paul also writes in Philippians 2:7 that Jesus took "the form of a servant, being born in the likeness of men." Peter objected to this because he didn't understand what Jesus was trying to do (Jesus says this to his face in John 13:7), which is totally within his character. 

(all references in RSVCE)