Que is here a subordinating conjunction; in French, you cannot omit them like in English. In your example, you should write:

Ce n’est pas une surprise qu’elle ne les aimait pas.

Note that the pas is necessary too (or it sounds very literary and old fashioned), and that the que becomes qu’ before a vowel.

Just putting this here because the formatting won’t really fit in a comment, not trying to replace the (good) answer.

For the record, while you can sometimes omit the “that” in English, it’s slightly context-dependent. Imagine, par example:

Personne «A»: She threw them away!
Personne «B»: It’s no surprise, she didn’t like them!

The sentence without “that” in it can mean something quite different – in this particular case the missing word can be implied to be “because”.