The time for the vicar to raise any question of methods of laundry for this item would be before handing it over, such particular arrangements are certainly not common knowledge.
It sounds to me as though the vicar is laying-off his guilt onto Eliza, who can politely but firmly decline it. Her mistake (if such it was, though that seems debatable at best) was caused by his neglect of his duties as he sees them.
Of course if the criticism is coming from the ousted "elderly lady" (or even worse, from someone who has decided to be offended on her behalf) then a whole new set of politics comes into effect. The only way to win that game is not to play.
Ironing a square into 9 smaller squares isn't rocket science, check if he wants it starched (I am guessing yes, it helps the cloth to 'stand', and will reduce soiling between washings). Of course this presupposes that he lets you touch it again.
The offended party could always replace the cloth, and make suitable arrangements for future ritual purifications, if (s)he feels sufficiently motivated, otherwise it might be time for him/her to
wind in his/her neck practice a little humility.