Edgar Villamar and his two children incurred the wrath of the home side's ultras by displaying their support for the league leaders.
The angry exchange, which saw Osasuna fans trying to take the flag away from the kids, was captured on television by La Sexta and sparked outrage among Spain's footballing community.
Villamar, though, has now revealed that Butragueno has offered him tickets to a Madrid home game, while Osasuna have issued a formal apology for the incident.
"The club would like to acknowledge the horrendous behavior observed in the television recording and point out that it is obviously completely unrelated to other Osasuna fans," a statement on the club's website read.
"It has nothing to do with the exemplary way in which our fans behave inside our stadium and encourage our team."
Madrid are currently six points clear at the top of La Liga, while Osasuna sit sixth.
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