In some places I believe it was a symbol of her morality. "Virtuous women" would tear the veil from the heads of prostitutes, so if a widow had children, likely she needed the veil as a form of attestation that she was a moral person.
What the commission meant I have no idea, unless the veiling was being done for religious profession. (Many widows "took the veil" as a statement that they had no desire, or intent, to marry again.) My research into mediaeval times (years ago) indicated that a widow normally veiled herself, while the unmarried girls/women making profession were veiled by clergy.