Jamieson, Fausset and Brown on Revelation 22:14

14. do his commandments--so B, Syriac, Coptic, and Cyprian. But A, Aleph, and Vulgate read, "(Blessed are they that) wash their robes," namely, in the blood of the Lamb (compare Re 7:14). This reading takes away the pretext for the notion of salvation by works. But even English Version reading is quite compatible with salvation by grace; for God's first and grand Gospel "commandment" is to believe on Jesus. Thus our "right" to (Greek, "privilege" or "lawful authority over") the tree of life is due not to our doings, but to what He has done for us. The right, or privilege, is founded, not on our merits, but on God's grace.

through--Greek, "by the gates."