Dear @Pkd12121,
Although your quarry has been well replied. I would like to supplement my opinion on this issue, just because you mentioned a twinge of guilt for not remembering date when your mother departed.
Our learned people has advised this period of 15 days for Pitr Paksha to pay our homage to our ancestors. They have recommended various Dos & Don’ts for performing Shraadh. There are rituals, processes, austerity and charity. But the prime idea of Shraadh is given just 3 posts above by Puneet ji – Shraddha (well said Puneet ji). If you have reverence or obeisance towards your ancestors, then time, day, month & year does not matter. You do not need to wait for a crow to accept the food or a brahmin to become bridge between the two dimensions.
Despite, there is a provision of offering your homage on the day of Amavasya, for the souls whose date of departure is not known, still if your bhava (emotion) is there, you may offer it to the departed any day. Take it from me, the soul would be very happy. Please do not have any kind of guilt for not knowing the date, I guarantee most of the people do not even know names of their forefathers including me (I know their names till 3 levels before my grandfather).
At this juncture, I wish to share something very personal with all. People wait for Pitr Paksha days to come so that they may offer their obeisances……..I do it everyday throughout the year. I may sound crazy but with VK with me I do it every day. Let me tell you how. Every morning after my prayers, when I water Tulasi plant at my home, I stand beside it, putting both of my hands together in a cup shape, imagine a holy Peepal tree and offer my reverence towards my forefathers, then feel as if my hands are filled with pure Ganga jal with some black Sesame & Tulasi leaves floating. With all my intentions concentrated, I offer this water (in imagination) filled in my hands to the base of Peepal tree that I am imagining and pray to the divine to give peace to my forefather’s souls and merge it to HIS enlightened energy.
Hope I am clear in my opinion and that you will not have any guilt in your mind anymore.