O my beloved Umlaut! … and all the characters I never wanted to know about … €¶Ŧ←↓→ØÞ¨ÆßÐŊĦĸŁ …
Copy and paste of non-standard ASCII text in Quanta can be cumbersome as the automatic replacement plugin only works with typing (Settings->Configure Quanta…->Automatic replacement of the accented characters). Another option would be to do some batch search-and-replace.
KFileReplace works both as a standalone app and a Quanta plugin (I don't think there is a Kate plugin yet). Multiple strings can be replaced directory-wide in one go, the session format is XML. I just googled a special character map (for reference, see e. g. here), wrote the .kfr XML file with a spreadsheet editor, and loaded it from KFileReplace. (Search/Replace->Strings->Load Strings List From File...)
Warning: Alpha-Howto! This has not been tested rigorously and might do some unwanted replacements; neither can it be a comprehensive list (e.g. no Greek characters except µ, sadly, I also decided against Chinese). Also, KFileReplace overwrites your original file (no undo!). I strongly recommend to enable "Do backup copy instead of overwrite" in the "Customise Search/Replace Session" dialog.
Whoever finds another culprit in the replacement list, please leave a comment.