My girlfriend broke up, but a month later she sent a text message saying that she missed me very much. Should I reply to her? Or pretend not to see it.

Go back if you want, as long as you are both single now.

She also sent you a message saying that she missed you. Maybe she is not used to not having you, or maybe she really can't let you go. If there is no contradiction in principle, she might as well give the other party a chance to communicate and figure out what she means before making plans.

If you really don't consider getting back together, then make it clear as soon as possible and let her give up.