Question てっと

桐葉「雪妃エレナは分かるんだけど、今日も逢桜は休み？」
ゆめみ「作業日なのに３日もサボリとか……逢桜さんらしくないよね」
寿季「とはいえLIMEに既読もつかないしな……桐葉の方はどう？」
桐葉「私も連絡したけど、なしのつぶてよ。茶店のほうも臨時休業中の張り紙があったし」
寿季「とりあえず心配だから、一言でもいいからメッセージが欲しいってLIMEに書いてっと」

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I understand the last sentence means "I would send her a Lime that I would like a message, even if it's just a word.", but I don't know about the てっと part. Could you please explain this usage of てっと (at the end of a sentence)?

よろしくお願いします。

It's just 書いて (the -て form used as a gentle/casual command) followed by the quotative と.
The っ is just there as a transliteration of how it would sound in casual speech (i.e. it's not that 「てっと」 is some kind of formal/official grammatical pattern or sentence-ending particle in itself.)