您没有引用-name属性，因此它将扩展为已存在的文件名。
无论如何，我会相当广泛地重构这个。Don't parse ls output，也许通过使什么时候引用和什么时候不引用变得更明显来简化这个问题。
未经测试，但仍有希望隐约有用：

#!/bin/bash

backup=/media/nfs/backup
backuplog=$backup/backup_delete.log
# no need to touch if you write to the file anyway
date +"Date: %C" >> "$backuplog"

# Avoid using a variable, just loop over the stems
for stem in takrib_golive takrib_golive_filestore.tar
do
    # echo $filename
    # Avoid parsing ls; instead, loop over matches
    for filename in "$backup"/*_"$stem".gz; do
        pattern="*_$stem.gz"
        if [ -e "$filename" ]; then
            echo "backup files exist"
            if files=$(find "$backup" -maxdepth 1 -mtime +3 -false -o -name "$pattern" -print -delete)
            then
                echo "The following backup file was deleted" >> "$backuplog"
                echo "$files" >> "$backuplog"
            else
                echo "There are no $pattern files older than 3 days in $backup" >> "$backuplog"
            fi
        else
            echo "No $pattern files found in $backup" >> "$backuplog"
        fi
        # Either way, we can break the loop after one iteration
        break
    done
done
# no need to explicitly exit 0

for + if [ -e ... ]的排列有点笨拙，但这就是检查通配符是否与任何文件匹配的方法。如果通配符不匹配，if [ -e将检查文件名实际上是通配符表达式本身的文件，并失败。