Steps to replicate the issue (include links if applicable):

• First reported in a module removing the "residence" parameter from infobox officeholder, using RemoveTemplatePaameter.
• Apply to a box with a residence parameter containing | in a quoted string

What happens?:
A mangled parameter is left behind. Reported in English Wikipedia [[Special:Diff/1348415854]].

What should have happened instead?:
The entire parameter is removed.

Other information (browser name/version, screenshots, etc.):
AWB 6.5.0.0 and earlier

This fix works in the reported case, but should be reviewed for possible other malignant cases: in Tools.PipeCleanedTemplate(), before the return add

if (restoftemplate.Contains("\""))
    restoftemplate = ReplaceWith(restoftemplate, QuotePair, RepWith);

where QuotePair is the regex "\".*?\"".