That's some JSON data that is, with an extra } at the end.

Here's an example of how you can load that JSON data as a Perl data structure, then delete items from it, by name, then re-encode the data structure back into a JSON string. Note it's an array reference of hash references:

use warnings;
use strict;

use JSON;

my $json;

{
    local $/;
    $json = <DATA>;
}

my $data = decode_json $json;

for my $entry (@$data){
    delete $entry->{absoluteLimits};
}

$json = encode_json $data;

print $json;

__DATA__
[{"absoluteLimits":{"conditionalLimits":{"bidirVolume":4096000,"name":
+"Home"},"resetPeriod":{"volume":"monthly day 15 00:??"}},"sliceVolume
+":5120,"subscriptionDate":"29-09-2016"},{"absoluteLimits":{"condition
+alLimits":{"bidirVolume":102400000,"name":"Home"},"resetPeriod":{"vol
+ume":"2400 hours"}},"description":"Promotion_tariffbasic:29-09-2016,0
+8-01-2017T10:21","name":"1004","sliceVolume":5120,"subscriptionDate":
+"30-09-2016T09:21"}]
[download]

Output:

[{"subscriptionDate":"29-09-2016","sliceVolume":5120},{"name":"1004","
+subscriptionDate":"30-09-2016T09:21","sliceVolume":5120,"description"
+:"Promotion_tariffbasic:29-09-2016,08-01-2017T10:21"}]
[download]