Any of your papers that were published after the 1 April 2016 will be flagged by Symplectic Elements as potentially falling within the REF Open Access policy. The REF Open Access policy only applies to papers accepted after the 1 April 2016 and therefore Symplectic Elements needs the acceptance date in order to work out if your paper is within the scope of the policy.
You need to enter the dates manually because many publishers are not supplying this information in their metadata and therefore Symplectic Elements cannot automatically retrieve this information. If you are unsure of the acceptance date, see if it is listed on the pdf of the published paper or on the journal's webpage for your paper. It is up to authors to enter this information into Symplectic Elements.