php - Regex match the double quote in BBCode attribute

I have text stored in my phpbb3 forum database with some incompatible bbcode such as the following:

Some text with [COLOR="red"]colored text[/COLOR] and [SIZE="7"]Big fonts[/SIZE] while "This double quote" is not matched

What I want is a regex that match any double quotes " " with any string inside them while those double quotes are inside the square bracket [ ] of the bbcode.

I need this to be able to fix those bbcodes by stripping the double quotes. The regex implementation is going to be using PHP.

Answer

You may be looking for something like this:

$code= 'Some text with [COLOR="red"]colored text[/COLOR] and [SIZE="7"]Big fonts[/SIZE] while "This double quote" is not matched';

preg_match_all('/\[.*?="(\w+)"\]/', $code, $matches, PREG_PATTERN_ORDER);
for ($i = 0; $i < count($matches[1]); $i++) {
    echo $matches[1][$i]."\n";
}

DEMO:
https://ideone.com/LEZHgx