Because the Septuagint diverged from the Hebrew text as both were copied and recopied over centuries, restoring or even just describing what it originally said became a scholarly problem in its own right, and one of the earliest attempts to address it was also one of the most ambitious works of the ancient world. In the third century CE, the Christian scholar Origen compiled the Hexapla, a six column comparison setting the Hebrew text, a Greek transliteration of it, and several Greek translations, including the Septuagint, side by side, marking every place the Septuagint added to or omitted from the Hebrew column. Most of that enormous work is now lost, known only through fragments and quotations, but it shows the tension between the Greek and Hebrew texts was recognized and studied within a few centuries of the Septuagint's own composition rather than only in modern scholarship.
Modern textual criticism reopened the question with new evidence: the Dead Sea Scrolls, discovered in the twentieth century, included Hebrew manuscripts of some books, notably Jeremiah and Samuel, that agree with the Septuagint's Greek against the later, standardized Masoretic Hebrew text, showing that in places the Greek translators were working from a genuinely different and sometimes older Hebrew original rather than simply mistranslating the text later Judaism settled on.