Hello HDTVJohn, and welcome to the Monastery!

Here’s my take on your problem, a variation on GrandFather’s solution:

#! perl
use strict;
use warnings;
use utf8;

while (<DATA>)
{
    chomp;

    my ($timecode, $text) = m!^\\ TC:  (\d{2}:\d{2}:\d{2};\d{2}) (.*)$
+!
        or die "Unexpected line: '$_'";

    if ($text =~ m!÷\w{4}!)
    {
        $text =~ s!^(?:÷\w{4})+(.*?)$!$1!;
        print "\n\\ TC:  $timecode $text";
    }
    else
    {
        print $text;
    }
}

print "\n";

__DATA__
\ TC:  16:12:48;28 ÷1426÷1426÷142D÷142D÷1470÷1470AND W
\ TC:  16:12:49;08 HI
\ TC:  16:12:49;11 LE
\ TC:  16:12:49;14  OVER
\ TC:  16:12:49;19  T
\ TC:  16:12:49;21 HE L
\ TC:  16:12:49;24 AS
\ TC:  16:12:49;27 T 10
\ TC:  16:12:50;07 ÷1426÷1426÷142D÷142D÷1470÷1470YEARS
\ TC:  16:12:50;17  W
\ TC:  16:12:50;19 E'
\ TC:  16:12:50;21 VE M
\ TC:  16:12:50;25 AD
\ TC:  16:12:50;27 E
\ TC:  16:12:51;09  MAJ
\ TC:  16:12:51;13 OR
\ TC:  16:12:52;22 ÷1426÷1426÷142D÷142D÷1470÷1470INVESTMENTS
[download]

Output:

14:49 >perl 945_SoPW.pl

\ TC:  16:12:48;28 AND WHILE OVER THE LAST 10
\ TC:  16:12:50;07 YEARS WE'VE MADE MAJOR
\ TC:  16:12:52;22 INVESTMENTS

14:49 >
[download]

Hope that helps,