We present an exploratory qualitative study to understand how writers interact with next-phrase suggestions. While there has been some quantitative research on the effects of suggestion systems on writing, there has been little qualitative work to understand how writers interact with suggestion systems and how it affects their writing process - specifically for a non-native but English writer. We conducted a study where amateur writers were asked to write two movie reviews each, one without suggestions and one with. We found writers interact with next-phrase suggestions in various complex ways - writers are able to abstract multiple parts of the suggestions and incorporate them within their writing - even when they disagree with the suggestion as a whole. The suggestion system also had various effects on the writing processes - contributing to different aspects of the writing process in unique ways. We propose a model of writer-suggestion interaction for writing with GPT-2 for a movie review writing task, followed by ways in which the model can be used for future research, along with outlining opportunities for research and design.