Você pode fazer isso com uma pequena modificação
(canalize a saída find para o loop while fazendo uma leitura )
Time=+30
PATH_TO_DUMP=/home/tarun/Desktop/Backup
#Find any Backup File defined by the time constraint
find $PATH_TO_DUMP -type f -mtime $Time | while read file
do
#To verify if $file is empty or has some value
if [ ! -n "$file" ]; then
echo "No Earlier Backups were found to compress" >> $PATH_TO_LOG
else
echo "Earlier Backups $file will be compressed" >> $PATH_TO_LOG
gzip "$file"
fi
done