I applied to work at a company about a month ago and started their interview process. Finally got the offer today and noticed that they plan to do a background check based on my resume.
However, the resume they're checking with is out of date and I was asked to leave the last company I worked at. Should I proactively send an updated resume to the recruiter upon accepting the offer, explaining the situation, or should I simply accept the offer as it's made and not say anything?

I feel like it's good to be honest, but I also don't want to attract the wrong kind of attention.

Please note: I know there's a similar question out there that asks what to do if you come in for an interview after being let go. What makes my situation different is that this got all the way to an offer.

I also see a similar question asked by someone ho changed jobs on their resume. My question s a bit different because I as asked to leave. 

Just to add, while I was asked to leave, it was on as good terms as possible (my former manager, who was also the company CEO, even wrote a positive letter of reference) though I'm not sure if it's wise to bring that up.

Update: Sent in a new copy of my resume, turned out to not be a problem at all.