only warn for anon functions

src/data/writing_datatypes.jl

@@ -446,6 +446,11 @@ end
 
 function h5convert!(out::Pointers, ::DataTypeODR, f::JLDFile, T::DataType, wsession::JLDWriteSession)
     t = typename(T)
+    if T <: Function && Base.isgensym(nameof(T.instance))
+        @warn LazyString("Attempting to store ", T, ".\n",
+                         "JLD2 only stores functions by name.\n",
+                         " This may not be useful for anonymous functions.")
+    end
     store_vlen!(out, UInt8, f, unsafe_wrap(Vector{UInt8}, t), f.datatype_wsession)
     if isempty(T.parameters)
         h5convert_uninitialized!(out+odr_sizeof(Vlen{UInt8}), Vlen{UInt8})
@@ -627,9 +632,6 @@ end
 # fieldodr, but actually encoding the data for things that odr stores
 # as references
 @nospecializeinfer function odr(@nospecialize(T::Type))
-    if T <: Function
-        @warn LazyString("Attempting to store ", T, ".\n Function types cannot be propertly stored in JLD2 files.\n Loading may yield unexpected results.")
-    end
     if !hasdata(T)
         # A pointer singleton or ghost. We need to write something, but we'll
         # just write a single byte.