Debate portals and similar web platforms constitute one of the main text sources in computational argumentation research and its applications. While the corpora built upon these sources are rich of argumentatively relevant content and structure, they also include text that is irrelevant, or even detrimental, to their purpose. In this paper, we present a precision-oriented approach to detecting such irrelevant text in a semi-supervised way. Given a few seed examples, the approach automatically learns basic lexical patterns of relevance and irrelevance and then incrementally bootstraps new patterns from sentences matching the patterns. In the existing args.me corpus with 400k argumentative texts, our approach detects almost 87k irrelevant sentences, at a precision of 0.97 according to manual evaluation. With low effort, the approach can be adapted to other web argument corpora, providing a generic way to improve corpus quality.