"Jesus charged the man not to make known the work that had been wrought, but straightway to present himself with an offering at the temple. Such an offering could not be accepted until the priests had made examination and pronounced the man wholly free from the disease. However unwilling they might be to perform this service, they could not evade an examination and decision of the case. DA 264.1"
The EGW passage explains the reason for Jesus' instruction to the healed leper, directly referencing the Levitical law regarding leprosy as outlined in Leviticus 14:2.
Leviticus 14:45-47"And he shall break down the house, the stones of it, and the timber thereof, and all the morter of the house; and he shall carry them forth out of the city into an unclean place. Moreover he that goeth into the house all the while that it is shut up shall be unclean until the even. And he that lieth in the house shall wash his clothes; and he that eateth in the house shall wash his clothes."
"So, too, if a house gave evidence of conditions that rendered it unsafe for habitation, it was destroyed. The priest was to “break down the house, the stones of it, and the timber thereof, and all the mortar of the house; and he shall carry them forth out of the city into an unclean place. Moreover he that goeth into the house all the while that it is shut up shall be unclean until the even. And he that lieth in the house shall wash his clothes; and he that eateth in the house shall wash his clothes.” Leviticus 14:45-47 . MH 278.3"
Ellen White directly references Leviticus 14:45-47 in this passage.