Instead of thinking in terms of "removing lines," think of it as, "print the rest of the lines, skipping certain ones." Also, the array you read the file into is not the file. You have to print the results back out. The best method is usually to read line-by-line from the input file, printing to a new file as you go, then move that new file into place if necessary. So in pseudocode:

open inputfile for reading
open outputfile for writing
while get a line from inputfile
  split it into fields
  if the 8th field is >= -10 and <= 10
    print the line to outputfile
close the files
move outputfile to inputfile
[download]

If, for some reason, you can't print the results to a new file (perhaps you don't have enough disc space to accommodate two copies of the data at once), look into the tie function and related modules. They allow you to tie an array variable to a file, so that each line is one element of the array. Then you could splice elements you don't want out of the array, and those lines will be removed from the file. But that method is more advanced, usually unnecessary, and more dangerous -- the "write to a new file then move it" method gives you a chance to make sure the new copy is what you wanted before wiping out the old copy.

I wondered whether using abs to get absolute value then making one comparison rather than two would be quicker. Apparently not.

use strict;
use warnings;

use Benchmark qw{ cmpthese };

my @data =
   map { rand( 20 ) * ( 1, -1 )[ int rand 2 ] }
   1 .. 1e6;

cmpthese(
   -10,
   {
       abs => sub { my @arr = grep { abs $_ <= 10 } @data },
       two => sub { my @arr = grep { $_ >= -10 and $_ <= 10 } @data },
   }
   );
[download]

      Rate abs two
abs 5.11/s  -- -9%
two 5.62/s 10%  --
[download]

Ha, yeah, it doesn't look like too big of a difference in terms of computation time. Interesting.

Canonical answer from aaron_baugher: Think in terms of writing your original content to a new file with some elements removed.

BUT, re your narrative: Your phrase "the 8th column" should be "the 9th column" because your removal target is column 9. Just so it's clear, column 9 is the 8th element, $dataline[8], of an array (@arr) formed by splitting

XP.sta1    -41.5166    0.0513    0.6842    0.1794    0  CPHI.BHZ   300.2458   -42.2436

on white space because "XP.sta1" is $line[0].

my $dataline = "XP.sta1    -41.5166    0.0513    0.6842    0.1794    0
+  CPHI.BHZ   300.2458   -42.2436";

my @arr = split /\s+/, $dataline;

say "$arr[0], \t $arr[8]";

=head  OUTPUT:

XP.sta1,         -42.2436

=cut
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UPDATE: Your pseudocode (I hope it was intended as pseudocode) is far from actually useful and makes very little sense in terms of your problem statement. Something on this order might serve you better:

use 5.018;
use Data::Dumper;

my $mFile='DATA1127720.txt';  # OP's sample data

open(my $tablec, "<", "$mFile") or die "Can't open the datafile: $!";
my @tablec = <$tablec>;

for (@tablec) {
    my @XPinfo = split /\s+/, $_;
    chomp @XPinfo;
    my $delayTime = $XPinfo[8];
    if ( $delayTime < -10 ) {
        say "\t OUT OF BOUNDS!!!  \$delayTime: $delayTime";
    }else{
        say $delayTime;  # revision to save desired lines left as an e
+xercise
    }
}

=head EXECUTION

D:\>perl 1127720FIXED.pl
         OUT OF BOUNDS!!!  $delayTime: -42.2436
2.5545
2.6160
2.6006


=cut
[download]

Your questions will benefit from careful use of language. Your "code so far" could be read as reflecting the PM admonition 'show us your code' ONLY if it accurately reflected your question ...and were it compilable.