Can we use GTEx data as control data for TCGA data? I am using Recount2 TCGA data and was wondering is it right to use GTEx data as control data for this. I would really appreciate your views on this?
Definately not directly. Probably not even if used indirectly. Different projects, done at different times, with different protocols, different machines, different library preps etc. 

We have tested combining GTEx and TCGA data for several different purposes where one might expect the analyses' internal controls would have allowed compatibilty, but even then we have always found a persistent batch effect which we were unable to remove.