The immigration and protection tribunal heard the couple felt bullied and claimed their belongings had been deliberately damaged by bleach.
"She found herself in an untenable and stressful environment," her lawyer told the tribunal.
"Her attempts to resolve the difficulties had been unsuccessful and, given the national Covid-19 lockdown, there were limited opportunities for her to distance herself from the situation. Her offending was impulsive: a retaliatory prank which unfortunately and unexpectedly backfired."
At her sentencing in October, the judge accepted that the appellant did not have any real appreciation that anyone would use the shampoo, thinking they would smell the bleach and not use the products.
But the landlady did, and an underlying medical condition of damaged nerves put her eyesight at risk, although medication led to a successful recovery.
The 30-year-old was served with a deportation liability notice after having been discharged without conviction and ordered to pay compensation of $771.
"It is accepted that the appellant's return to Argentina will be very distressing and disappointing for both the appellant and her partner," said the tribunal in its ruling.
"The partner will have to make a decision about how he will manage their future relationship against his desire to remain in New Zealand.
"They both feel that the situation is unfair because deportation appears to them to be a harsh and unfair response by the immigration system to the appellant's aberrant behaviour. Certainly the sentencing judge who considered that behaviour took the view that it would be disproportionate for it to affect her immigration status."
But it said the High Court had ruled previously there was a high threshold for a finding of exceptional circumstances of a humanitarian nature.
"While her circumstances are genuinely concerning, they are not well outside the normal run of circumstances."
