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This is pretty common in old* Siddurim. You can see omitting just ועל בריתך שחתמת בבשרינו on Hebrewbooks here here here here and here and on Hebrewmanuscripts.org manuscript #747. You can see omitting that phrase plus ועל תורתך שלימדתנו on Hebrewbooks here and on Hebrewmanuscripts.org manuscript #1762. This siddur is not clear how much exactly to omit. ...
The Italian nusach Bnei Roma omits ועל בריתך שחסמת בבשרנו for women.
Tashlumin always has to be after an ordinary obligatory prayer, so in your case in order to say the Tashlumin she would have to Daven Maariv first and then say the Tashlumin. (Halichot Shelomo Tefillah chapter 13 footnote יא)
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