Recent work in cross-lingual contextual word embedding learning cannot handle multi-sense words well. In this work, we explore the characteristics of contextual word embeddings and show the link between contextual word embeddings and word senses. We propose two improving solutions by considering contextual multi-sense word embeddings as noise (removal) and by generating cluster level average anchor embeddings for contextual multi-sense word embeddings (replacement). Experiments show that our solutions can improve the supervised contextual word embeddings alignment for multi-sense words in a microscopic perspective without hurting the macroscopic performance on the bilingual lexicon induction task. For unsupervised alignment, our methods significantly improve the performance on the bilingual lexicon induction task for more than 10 points.