The division bench of Justices P B Majmudar and A V Mohta directed the ASI to maintain a status quo till further orders.
Petitioner Sunanda Sitad approached the High Court after the ASI issued her a demolition notice in February, alleging that the house was an encroachment.
The petition says that she and her son, who works on a contract basis for the ASI, live in this house, and they fall in below-poverty-line category.
She claims that her family has been living in the house for the last 100 years, and in fact her late husband looked after the Buddhist structure which attracts devotees.
ASI lawyer, advocate Aniket Nikam, however argued that the house was unauthorised, and it stood on a protected site.
Asking the ASI to show sympathy to the petitioner, Justice Majmudar said, "Even Gautam Buddha renounced the world after seeing poverty and misery".
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The Court posted the matter for further hearing on June 13, and also issued notice to the Vasai-Virar Municipal Corporation (in whose jurisdiction the site lies), seeking its reply.
Sitad has demanded that either the demolition notice be set aside, or her family be rehabilitated elsewhere.