Try the following more generic version which strips the first three maximum recursive match of square brackets...

#!/usr/bin/perl -w
use strict;

my $re;
$re = qr/
    \[ # Opening bracket
    (?:(?: # Capture the content and then forget it
        [^\]\[]+
        |
        (??{$re}) # Or recurse
    )+) # and allow repeats internally
    \] # Closing bracket
    /x;

while (my $line = <DATA>) {
    $line =~ s/($re){3}//g;
    print $line;
}


__DATA__
[Microsoft][ODBC SQL Server Driver][SQL Server][0122]USAGE: InvokeStor
+edProcedure [param1], [param2], [param3], [param3]
[[B1] [B2]][[B3]][B4][B5]Stuff....
[download]

And the output is as expected:

[0122]USAGE: InvokeStoredProcedure [param1], [param2], [param3], [para
+m3]
[B5]Stuff....
[download]