Dame Elish stood down as Scotland's top prosecutor last year and was awarded a tax-free "resettlement grant" worth £28,000.
She has since taken a prestigious post at St Hugh's College, Oxford University.
Crown Office chiefs said Dame Elish, the first woman to become Lord Advocate, was entitled to the pay-out under Holyrood rules.
However, criticisms have been made of the five-figure "golden goodbye", revealed in the Crown Office's latest annual accounts.
A spokeswoman for campaign group Taxpayer Scotland said: "There should be serious questions about why this was paid and why it was so much.
"Our legal profession is always complaining about the lack of money in the court system, so why was it necessary to make this payment to a person who was leaving of their own accord to pursue other opportunities?
"It's always a worry when we find these things buried in reports."
The grants are traditionally given to MPs, MSPs and Government ministers after they leave office.
Dame Elish, originally from Govan, Glasgow, has gone on to work in a number of posts, including chairing a Government commission on female offenders.
She is a member of the firm of advocates Terra Firma and a visiting professor at Strathclyde University.
She was highly regarded during her time as Lord Advocate for her commitment to tackling domestic violence and other crimes against women.