Edit-based text simplification systems have attained much attention in recent years due to their ability to produce simplification solutions that are interpretable, as well as requiring less training examples compared to traditional seq2seq systems. Edit-based systems learn edit operations at a word level, but it is well known that many of the operations performed when simplifying text are of a syntactic nature. In this paper we propose to add syntactic information into a well known edit-based system. We extend the system with a graph convolutional network module that mimics the dependency structure of the sentence, thus giving the model an explicit representation of syntax. We perform a series of experiments in English, Spanish and Italian, and report improvements of the state of the art in four out of five datasets. Further analysis shows that syntactic information is always beneficial, and suggest that syntax is more helpful in complex sentences.