That is the breather or "PCV" baffle built into the valve cover. It has nothing to do with EGR. It also will have nothing to do with your valve being oily - think about it - oil is sprayed around constantly inside the valve cover.

EGR is Exhaust Gas Recirculation. It is the valve that opens between the exhaust manifold and the supply pipe to the crossover pipe. The point is to introduce exhaust gas into the intake air stream to lower the temperature of combustion and drop the NOx level of the exhaust gas. There shouldn't be any oil in the EGR system, any oil will be coming from the breather tube or from the turbo seals leaking.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]