Lots of academic papers have been written on the translation of L'étranger's first paragraph into English, and, cela ne veut rien dire has been translated differently according to the translator's analysis and comprehension of the novel. This can be seen in this 1988 article in the New York Times which gives two different translations for cela ne veut rien dire.
Since on FL we are asked to answer with facts rather than opinions I will try and give you a few keys to decide for yourself which translation you prefer.
The opening paragraph of L'étranger has been endlessly discussed in critical essays and it can only be understood in relation to the entire novel. As you have pointed out cela ne veut rien dire is a recurring sentence in the novel1. These first few lines help characterize Meursault's indifference. A key theme of the novel is Meursault's emotional indifference and his detachment to the society that surrounds him. When reading this first paragraph we must have in mind that L'étranger is Camus's first work in his cycle of the absurd2.
This sentence is a first step in showing Meursault's indifference to his mother's death, a few lines later he is depicted remaining indifferent at his mother's burial. This is central to Meursault's character. In 1942 (the year the novel was published) Camus said:
In our society, any man who does not cry at his mother's funeral risks being sentenced to death3. (My translation)
And indeed, this is what happens to Meursault in the end.
Two different meanings have been given to this "cela ne veut rien dire": it can either refer to the meaninglessness of the information about the date on which Meursault's mother died, or it can mean that Meursault is indifferent to his mother's death4.
According to which interpretation you choose you will translate cela ne veut rien dire in this opening paragraph as "That doesn't mean anything" (Gilles's answer suggests "this is meaningless" that works well too here), that retains the ambiguity we have in French and lets the reader make their own decision; or "Which leaves the matter doubtful", which stresses on the meaninglessness of the information concerning the date.
As an aside I could point out that even the translation into English of the title of the novel is open to controversy. If you are interested you can listen to this leçon du collège de France: "The Stranger contre The Outsider : un combat pour le titre de L'Étranger"
1 The author of a critical essay on the indifference of Meursault counted sept fois l'expression « cela n'avait pas d'importance », cinq fois « cela m'était égal », plus quantité d'autres formules comme « cela ne veut rien dire », « cela ne signifiait rien » ou d'autres semblables.
2 Camus separated his work into three cycles. Each cycle consisted of a novel, an essay, and a play. The first was the cycle of the absurd consisting of L'Étranger, Le Mythe de Sysiphe, and Caligula. (From Albert Camus entry on Wikipedia)
3 Original sentence: Dans notre société, tout homme qui ne pleure pas à l'enterrement de sa mère risque d'être condamné à mort. You can find it here.
4 This is how these two theories have been summed up in Sparknotes: "Mersault’s comment, “That doesn’t mean anything,” has at least two possible meanings. It could be taken as part of his discussion about which day Madame Meursault died. That is, Meursault could mean that the telegram does not reveal any meaningful information about the date of his mother’s death. However, the comment could also be read more broadly, with a significance that perhaps Meursault does not consciously intend; Meursault might be implying that it does not matter that his mother died at all. This possible reading introduces the idea of the meaninglessness of human existence, a theme that resounds throughout the novel.