Assuming you want to replace it with some static value (well, you can always change this anyway), some kind of find and replace snippet like this can do the trick:
$content = apply_filters( 'the_content', $post->post_content);
// set the replacement string value
$replace = "REPLACEMENT";
// make sure the quotes used are exact
$find_start = "<param name="filter" " . 'value="';
$find_end = '"';
// find the (end of) search string start position
$pos = strpos( $content, $find_start) + strlen( $find_start );
// get the content before (end of) search string
$before = substr( $content, 0, $pos );
// get content after search string
$after = substr( $content, $pos, strlen( $content ) );
// strip the after-content before end quote
$pos2 = strpos( $after, $find_end );
$after = substr( $after, $pos2, strlen( $after) );
// recombine content with replacement value
$content = $before . $replace . $after );
return $content;