"My question is what on earth would Gertrude have been doing in India"
Familysearch.org
https://www.familysearch.org/ark:/61903/1:1:FGV5-3X9 has an entry for marriage in India in 1919 for Dorothy Gertrude Marchant father Charles John Marchant.
Is she connected to your Gertrude? As death certificates are only as accurate as the informant knows, perhaps the family assumed Charles was deceased but he may have already been institutionalised?
Also a possible passenger record for Charles? from Ancestry.com.au UK Inwards Passengers.
Name: Charles Marchant
Arrival Age: 55
Birth Date: abt 1878
Port of Departure: Karachi, Pakistan
Arrival Date: 1 Apr 1933
Port of Arrival: Liverpool, England
Ports of Voyage: Karachi; Bombay; Port Said and Marseilles
Ship Name: City of Baroda
Shipping Line: Ellerman City Line
Official Number: 140594
Name: Chas Rowse Marchant
Gender: Male
Admission Date: 27 Jul 1905 Discharge 1924
institution: Wandsth
Institution Place: Surrey, England Source UK Lunacy admissions.
Perhaps this is why she described herself as a widow?