The salutation by the hand of me Paul. Remember my bonds. Grace be with
Paul's autograph salutation (so 1 Corinthians 16:21; note, Galatians 6:11: cf. 2 Thessalonians 3:17, with 2 Thessalonians 2:2), attesting that this letter, through written by an amanuensis, is from himself.
Remember my bonds - already mentioned, Colossians 4:3, and Colossians 4:10 - an incentive to them to love and pray for him: still more, that they should, in reverential obedience to his monitions, shrink from the false teaching stigmatized, remembering what a conflict (Colossians 2:1) he had in their behalf amidst his bonds. 'His bonds moved over the paper as he wrote; his (right) hand was chained to the (left hand of the) soldier who kept him' (Alford).
Grace be with you - Greek, 'THE grace' which every Christian enjoys in some degree, flowing from God in Christ by the Holy Spirit (Titus 3:15; Hebrews 13:25).