How to save face and apologize after a text was taken the wrong way?

Interpersonal skills are the behaviors people use to interact well. You're blocked, that's the other person putting up a boundary. Respecting that boundary is the interpersonal skill that you could and should use to save face.

You've apologized to her in two places, presumably the rest of the group can see the apology you left her there. Leaving her alone is the best thing you can do for your image towards the rest of the group. Have healthy interactions with the rest of the group, don't gossip about what happened or complain that it's unfair that message is still up, and they're likely to forget about it soon. Respect the boundary, the block, and don't contact that person further. If anyone asks you can be honest: you made a mistake, you apologized and the boundary is clear and you're respecting it now.

I've had people online try to claim they're the victim of things I do, the best way I've found so far to handle that is to ignore it. Any attempt at telling those kinds of people they're not the victim, or that they're lying, has never ended well. Usually, I don't even have to stand up for myself, third parties step up to meddle whenever these people insist on forcing an interaction with me, because they can see the lies, they know I'm not like that. Healthy interactions with the rest of the Telegram group will likely have the same result for you, though the only variable here might be age. Your group might be a bit less mature than the groups I've had these experiences in.

If people block you, or ignore you, the best you can do is offer them the same courtesy. I can say that there's nothing more annoying than someone that keeps trying to force an interaction, after having violated your boundaries and you blocking them. Let her make the first move if she ever wants to interact with you again.