Wow this took me some time and all it was, was a stupid typo:
var data="action=update&ID="+rowid.ID+"&Rückruf="+rowdata.Rückruf + "&Kategorie="+rowdata.Kategorie+"&Bekannt="+rowdata.Bekannt+"&Relevant="+rowdata.Relevant+"&Priorität="+rowdata.Priorität+"&GVID="+$rowdata.GVID;
See the $ before the last variable? 🙂