First, Second, and Fourth Bracketed Letter of a Word

Question

What do the first, second, and fourth bracketed letters in "retreating," "the," and "to" indicate below? I've frequently encountered similar examples like these in others' writing. What exactly is meant by the use of brackets around the second letters of words?

Image below from http://dianahacker.com/pdfs/hacker-bish-cms.pdf — one of Diana Hacker's handbooks [reproduced under fair use]:

A Southern reporter traveling with Forrest makes clear that the discrimination was deliberate: “Our troops maddened by the excitement, shot down the ret[r]eating Yankees, and not until they had attained t[h]e water’s edge and turned to beg for mercy, did any prisoners fall in [t]o our hands . . . .

References given in the PDF are

¹⁸ Foote, Civil War, 111.
¹⁹ Cimprich and Mainfort, “Fort Pillow,” 304.
²⁰ Quoted in Wills, Battle from the Start, 189.

Answer 1

In that case they probably indicate that the letters are not in the original text, but that the editor has inserted them so that the passage makes sense.