One of the novel's paradoxes is that Camus employs a first-person narration, which normally allows the reader access to the character's inner thoughts and feelings (see e.g. Charlotte Brontë's Jane Eyre), but does not give us much insight into Meursault's thoughts and feelings. Meursault admits to the examining magistrate (Part Two, Chapter I) that he has lost the habit of questioning himself, and the rest of the novel bears this out. He is also indifferent to many things that people say to him, e.g. Marie's marriage proposal and Raymond's question whether he wants to be his pal.
Meursault's admission that he does not attach great importance to the question whether his mother died on the day he received the telegram or the day before is the beginning of the pattern of indifference that runs through the entire novel. (Near the end he even says that life is not worth living.)
From a purely technical perspective, Meursault is right in saying he does not know on which day his mother died. The telegram says the funeral will take the next day but does not say whether his mother died that morning, the day before or during the night. However, Meursault does not frame the issue in this way; instead of mourning about the loss of his mother and a plan to find out the day of her decease, we only get, "That doesn't mean anything."
If we accept Meursault's story (i.e. the novel as a whole) as what he truly thinks and feels, then he is not bothered by it. However, it is also plausible that he simply has no access to his inner feelings and that his seeming indifference is a symptom rather than the cause of his strange reactions. This might be connected to his focus on physical and sensory impressions that pervade the novel (see What is Meursault's problem with the heat?). This enigma appears to be related to Camus's artistic credo at the time, expressed both in his notebooks (Carnets) and in The Myth of Sisyphus: "The true work of art is the one that says less" ("Le véritable œuvre d'art est celle qui dit moins").
However, The Stranger has also been subjected to psychoanalytic interpretations, for example in the light of Freud's book Mourning and Melancholia (Trauer und Melancholie. According to Freud, mourning could one of two paths. (I am using Danielle Trudeau's article Mourning and Melancholia: Freud’s Thoughts on Loss here. See also pages 114-123 in Bernard Pingaud's book L'Étranger d'Albert Camus, Gallimard, 1992.) Either the person in mourning feels their loss in an external way. In that case, they can reform their feeling of loss and the process ends with a kind of acceptance. Or the person in mourning feels their pain in an internal way; it is felt in the unconscious, where the person is not aware of it. In that case, according to Freud, the grief is so heavy that it is repressed and cannot be processed by the conscious mind. This would explain why, at the funeral, Meursault behaves in a way that witnesses later describe as insensitive. It would also explain why his mother is mentioned again and again later in the book, for example, when he hears Salamano weep over the loss of his dog, he suddenly thinks of his mother but can't explain why (end of Part One, chapter III).
