This has been bothering me for some time, as in the OED Symbols guide there is no asterisk entry under Quotations (there is one in Etymologies but it’s clearly not relevant). Here’s an example, in the earliest OED cite for the phrase ‘pink elephant’.

1901 Washington Post 8 June 6/4 We extended to him [sc. an alcoholic] the helping hand, of course, but he shrank away, mistaking this for a *pink elephant.

I finally emailed OED and here’s the reply from Margot Charlton.

The purpose of the asterisk is to indicate the first use we have found of the phrase in question.  It is used in combination sections, where quotations run on from one expression to the next, and is intended to help the reader home in on successive combinations.

IIRC, that fact used to be easily found in the supporting online documentation.  They seem to be losing or hiding some useful information as they rework the help section.