Hello Roderick,
If the death cert record of her surname which you had on your phone was wrongly spelt, you could try contacting the Registry at the address at www.gov.im/registries/general/civilregistry/ and ask them to correct their records. You would need to post them copies of the documents you hold to prove your case.
If her name was incorrectly spelt in the parish register at her burial, I'm not sure that there is anything that could be done about that unless the vicar is still alive (unlikely). Ask for advice from the Registry when you write to them.
The spelling could possibly be changed in the IOM Family History Society burial transcripts, but they may be reluctant to do so if the transcript is correct. I'll ask them.
Is her gravestone also engraved incorrectly? I think you would have to approach the church directly about changing that.
Sue