You, like so many others, are not getting it. It is in IH's interest to get this supposed offer onto the docket where it can be made "real". If it's for a refund of only $1 then the judge can throw Rossi's case under the bus in a hundred ways. If it is for a real refund of the whole amount and IH declines, the judge can make IH's life difficult as well.
That makes this a pivotal issue in this trial. Whether or not Rossi used illegal aliens to install his supposed heat exchanger is not a pivotal issue.
If it was me, and if many, many people weren't 'getting' something I was saying, I'd seriously wonder if what I was saying made sense. But maybe that's just me.
Seriously, the "offer" is - at absolute best - a fringe issue of trivial importance. More likely, it's not relevant at all. In neither case is it a pivotal issue in the trial. There are substantial reasons to doubt that the offer - if it existed - can be admitted into evidence, and even if it is there's plenty of room for both sides to spin any offer to their advantage. (For example, if it was an offer for the whole amount, IH can spin a choice to decline as being based on factors such as their inability to know if Rossi had used their up-front money to advance the research and was now trying to push them out so he could obtain a better deal for the US license elsewhere.)
And that's setting aside your inexplicable belief that the judge would try to use that evidence to shape the outcome of a jury case.