Catalyzes the removal of the phosphate group from the phosphothreonine in the mitogen-activated protein kinases p38, phosphothreonine in the mitogen-activated protein kinases such as MAPK2/ERK2, MAPK3/ERK1, MAPK8 and MAPK14 in an irreversible reaction, thus preventing the downstream phosphorylation of histone H3. This epigenetic modification results in inhibition of the transcription of a specific subset of pro-inflammatory genes, and ultimately to a reduced immune response against the invading pathogen. The diminished immune response enhances the bacterium's ability to disseminate and multiply within the host (By similarity). Secreted via the type III secretion system (TTSS). Localizes in the nucleus of the infected cell (By similarity). Belongs to the phosphothreonine lyase family.