"To reconsider the matter" means to think about something again, possibly with the intention of changing one's previous decision, opinion, or perspective. Full definition
I am writing to ask you to reconsider this matter because terminating this support would have a profoundly negative effect on the survival and healthy development of thousands upon thousands of infants and young children worldwide. (infactcanada.ca)
The petition notes Loke is seeking to quash the decision allowing Trinity Western to grant law degrees or, in the alternative, have the minister reconsider the matter. (canadianlawyermag.com)
The CPS subsequently reconsidered the matter and sought a voluntary bill of indictment in respect of the same incident on the basis of the evidence that it had chosen not to use at the previous hearing. (newlawjournal.co.uk)