No Omega logo/symbol on vintage engraved Seamaster dial. Is this possible?

My father-in-law, long deceased, was given a commemorative engraved Omega Seamaster when he retired. There is no Omega logo/symbol on the dial, just the word Omega with Automatic centered below it. Then Seamaster in script is written and centered towards the bottom. It is gold or gold filled, no visible serial number on back but the back is also gold and it has the Seahorse with the Omega symbol and my Father-in-laws name engraved. It has a replacement Omega band but my husband said it came with a leather band originally. It has double straight lines at the quarter hours and single straight lines for each five minute interval otherwise. It has a second hand. I am concerned about no Omega symbol on the dial. Probably from the 50's-60's. Have you ever seen this before with no Omega logo on the face? I haven't opened the back. Too scared I will screw something up.

I will try and see if I can get better shots. I was just curious if Omega ever created dials without their symbol in the 50's or 60's.

Better photos of dial and back.

Did refinishing most likely remove the Omega symbol?

Thank you SOG53. You are correct. I love the watch regardless. I was just curious. It is a men's watch but not huge and it is very slim so I wear it all the time and it still keeps perfect time and the second hand works. It really is a lovely piece and will get passed to my father-in-law's great grandson of the same name...therein lies the value.