Tourists may have to wrestle with crowds on popular islands during peak season.

wrestle 是动词，本义是“摔跤、搏斗”，引申为“努力应对、费力解决”。在句中与 with 搭配，wrestle with 表示“与……作斗争、艰难应付”，强调面对困难或麻烦时需要付出很大努力。