While great progress has been made in non-English monolingual passage retrieval in recent years, there has been little work exploring influential factors behind cross-lingual transfer capabilities in monolingual passage retrieval. In a retrieval corpus such as Wikipedia, incidental multilingual texts occur in forms including code-switching, translated name entities, and so on. In this work, we study how these naturally occurring multilingual texts impact the cross-lingual transfer of dense retrievers on monolingual passage retrieval. Results on 41 pairs of languages suggest that the cross-lingual transfer capacity of dense retrieval can be largely achieved with no incidental multilingual text, yet the decrease in effectiveness is correlated with the number of queries and documents containing incidental multilingual text. This suggests that cross-lingual transfer can be achieved by semantic understanding of the inputs alone and further enhanced by manually injecting more overlapping lexicons ( https://github.com/Andrwyl/IMT-in-monolingual-IR ).