Or does it perhaps the judge may decide something different from the offer and the other side will not b able to refer to my letter of offer if it is titled without prejudice I am trying to put it in the layman language so I can understand the main thrust of the term
Sorry, I think you need someone with more legal knowledge than me on that.
My understanding of the without prejudice term is just what the writer is not surrendering any of their rights in the letter.
In the context you mentioned, my impression was just that the letter wouldn''t constitute any acceptance or refusal of the offer, or that in accepting/refusing an offer they were not banned from changing their mind later. (i.e. waiving their right to change their mind later).
I might be wrong, one of the legal professionals on here may correct me. They may also need more context than you''ve given at the moment.