"Peter saw in the collector's question an insinuation touching Christ's loyalty to the temple. Zealous for his Master's honor, he hastily answered, without consulting Him, that Jesus would pay the tribute. DA 433.1"
"And when they were come to Capernaum, they that received tribute money came to Peter, and said, Doth not your master pay tribute? He saith, Yes. And when he was come into the house, Jesus prevented him, saying, What thinkest thou, Simon? of whom do the kings of the earth take custom or tribute? of their own children, or of strangers? Peter saith unto him, Of strangers. Jesus saith unto him, Then are the children free. Notwithstanding, lest we should offend them, go thou to the sea, and cast an hook, and take up the fish that first cometh up; and when thou hast opened his mouth, thou shalt find a piece of money: that take, and give unto them for me and thee."
EGW directly refers to and interprets the events described in Matthew 17:24-27, specifically Peter's hasty response.
"But Peter only partially comprehended the purpose of his questioner. There were some classes who were held to be exempt from the payment of the tribute. In the time of Moses, when the Levites were set apart for the service of the sanctuary, they were given no inheritance among the people. The Lord said, “Levi hath no part nor inheritance with his brethren; the Lord is his inheritance.” Deuteronomy 10:9 . In the days of Christ the priests and Levites were still regarded as especially devoted to the temple, and were not required to make the annual contribution for its support. Prophets also were exempted from this payment. In requiring the tribute from Jesus, the rabbis were setting aside His claim as a prophet or teacher, and were dealing with Him as with any commonplace person. A refusal on His part to pay the tribute would be represented as disloyalty to the temple; while, on the other hand, the payment of it would be taken as justifying their rejection of Him as a prophet. DA 433.2"
"Wherefore Levi hath no part nor inheritance with his brethren; the Lord is his inheritance, according as the Lord thy God promised him."
Ellen White directly references Deuteronomy 10:9 in this passage.
"Only a little before, Peter had acknowledged Jesus as the Son of God; but he now missed an opportunity of setting forth the character of his Master. By his answer to the collector, that Jesus would pay the tribute, he had virtually sanctioned the false conception of Him to which the priests and rulers were trying to give currency. DA 433.3"
"And Simon Peter answered and said, Thou art the Christ, the Son of the living God."
Both passages refer to Peter's confession of Jesus as the Son of God. The EGW passage uses this confession as a backdrop to highlight Peter's later actions, creating a thematic link.
"professed people of God, were required to maintain His service; but Jesus, the Son of God, was under no such obligation. If priests and Levites were exempt because of their connection with the temple, how much more He to whom the temple was His Father's house. DA 433.4"
"He saith, Yes. And when he was come into the house, Jesus prevented him, saying, What thinkest thou, Simon? of whom do the kings of the earth take custom or tribute? of their own children, or of strangers?"
The EGW passage directly explains the principle Jesus teaches in Matthew 17:25 about the exemption of children from tribute. It's a direct application of the principle illustrated in the biblical text.