This is also mentioned in the article that you linked:

> In April 2016, during UN-brokered peace talks in Kuwait, Houthi representatives gave the United States a "sincere apology" for the "Death to America" slogan, claiming that the slogan was used for "domestic consumption as a means to attract support in the streets and create a common cause between their supporters to keep them united."

> During the Red Sea crisis, Houthi supporters waved the flag of Palestine every Friday during anti-Gaza genocide and anti-western attacks on Yemen demonstrations, alongside the slogan and flag of Yemen. A new Houthi slogan appeared after the group's re-designation as a terrorist organisation: "America is the mother of terrorism" set on a red background.

They did that just as they began the starvation siege of Taiz.