Do you mean TWiki or MediaWiki?
If I am not mistaken the TWiki syntax for italics is _italic_ while
''italic'' (with double single quotes) is MediaWiki syntax.

Using the proper input format for each syntax gives the expected results:

% pandoc -f twiki -t native
_italic_
[ Para [ Emph [ Str "italic" ] ] ]

% pandoc -f mediawiki -t native
''italic''
[ Para [ Emph [ Str "italic" ] ] ]

While mismatched input format—syntax does not work, which is also expected:

% pandoc -f twiki -t native
''italic'"
[ Para [ Str "''italic'\"" ] ]

% pandoc -f mediawiki -t native
_italic_
[ Para [ Str "_italic_" ] ]

It seems your wiki files are mediawiki instead of twiki, in which case you
should specify mediawiki as input format. In case you have a mixture of
both the presence of double and triple single quotes is a pretty sure
indicator that you have a mediawiki file.

Den ons 8 juni 2022 13:59'Léna Montenot' via pandoc-discuss <
pandoc-discuss-/JYPxA39Uh5TLH3MbocFFw@public.gmane.org> skrev:

> Hello,
>
> I want to use Pandoc to export some wiki articles towards a new platforms.
> However, whenever I'm converting a TWiki file to Markdown, while the bold
> sections are parsed correctly, the italics are being replaced from '' to
> \'\' which is not ideal to automate the process.
>
> Is there any fix available ? Thank you :)
>
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