Animals Taiwan

"Once you have a pet, the two most important things to remember are to neuter your pet so it can't further increase Taiwan's animal population and to train it properly"

I am not clear about the using of the "to".

Why is not "that" used in here? like:

 "Once you have a pet, the two most important things to remember are that neuter your pet so it can't further increase Taiwan's animal population and to train it properly"

Maybe I lack of some grammar tips about "to"........