Influenza-like illness (ILI) estimation from web search data is an important web analytics task. The basic idea is to use the frequencies of queries in web search logs that are correlated with past ILI activity as features when estimating current ILI activity. It has been noted that since influenza is seasonal, this approach can lead to spurious correlations with features/queries that also exhibit seasonality, but have no relationship with ILI. Spurious correlations can, in turn, degrade performance. To address this issue, we propose modeling the seasonal variation in ILI activity and selecting queries that are correlated with the residual of the seasonal model and the observed ILI signal. Experimental results show that re-ranking queries obtained by Google Correlate based on their correlation with the residual strongly favours ILI-related queries.