If the T-cells that have passed out of the lymph node, into the peripheral circulation, and then migrate into the inflamed tissue do encounter APCs presenting their corresponding peptide-MHC complex, then they begin their effector function. If the T-cells are CD4 T-cells, they will secrete cytokines that provide help. If the T-cells are CD8 T-cells, if they see any cells in the inflamed tissue that are presenting peptide-MHC 1 complexes, then they'll kill those cells.