首先,anytime是个副词（adv.） 表示：任何时候；总是；无例外地；在任何时候.很显然,副词是不可能引导一个句子.
anytime在这个句子中是做check out的宾语,所以后面跟的应该是一个宾语从句.而且是一个省略that的宾语从句.
宾语从句中that一般情况可省 ,但也并不是任何情况下都可以省略.
eg：宾语从句
1． 定义：用作宾语的从句叫宾语从句.
2． 构成：关联词+简单句
从属连词that.如：
He told us that he felt ill. 他对我们说他感到不舒服.
I know he has returned. 我知道他已经回来了.(that省略)
注:宾语从句中that一般情况可省 ,但that在引导宾语从句时也并不是任何情况下都可以省略.在以下情况下,that不能省略.
1． Everybody could see what happened and that Tom was frightened.(and连接两个宾语从句,that宾语从句放在and的后面时,that不能省略.)
大家都会看出所发生的事情并知道Tom非常害怕.
2．I know nothing about him except that he is from the south.(that引导的宾语从句作介词宾语时,that不能省略.)
对他我一无所知,只知道他是南方人.
3．That he ever said such a thing I simply don’t believe. (that从句位于句首时,that不可省略.)
我简直不相信他曾说过这样的话.
4． We decided, in view of his special circumstances, that we would admit him for a probationary period. (主句谓语动词与that从句之间有插入语,that不可省略.)