Given:

Aero Research Labs.###FundingOrg[###Date______[ Dec 1963
Aero Research Labs.###FundingOrg[ BBC###Date______[ Dec
[download]

if you want to delete everything starting with "###FundingOrg[" and ending with everything up to but not including the following "###", the following will do the trick:

while(<DATA>) {
    chomp($_);
    $_ =~ s/###FundingOrg\[.*?(?=###)//;
    print $_ . "\n";
}

__DATA__
Aero Research Labs.###FundingOrg[###Date______[ Dec 1963
Aero Research Labs.###FundingOrg[ BBC###Date______[ Dec
[download]

output:

Aero Research Labs.###Date______[ Dec 1963
Aero Research Labs.###Date______[ Dec
[download]

hope this helps,
davidj