The snapshot distribution of mRNA counts per cell can be readily measured using single molecule FISH or single-cell RNA sequencing. These distributions are often fit to the steady-state distribution of the two-state telegraph model to estimate the three transcriptional parameters for a gene of interest: the rate of transcription, the rate of switching to the active transcriptional state and the rate of switching to the inactive state. These parameters are often understood as being reflective of the average cell in a population. However it is currently unclear to what extent does the cell-to-cell variation of parameters (extrinsic noise) affect the accuracy of parameter estimation. Here we develop an analytical approach to understand the factors determining the size and sign of estimation bias. We find bias signatures that depend on the source of extrinsic noise and the mode of transcriptional activity. We estimate the size of extrinsic noise from the covariance matrix of scRNA-seq data which we use to correct published estimates of parameters for mammalian genes.