Math PhD after graduating with average grades

This is the sort of thing you won't know until you apply and someone with authority to decide evaluates your background. However, in general, your most recent work will weigh more heavily in a decision for most people who think about it for more than a minute.

However, you are in competition with others who don't have your "disadvantage" so you need to have some way to explain it. If your recent work overwhelms the past then you are more likely to be successful.

A doctoral advisor will be more interested in your potential for the future than in your past and will be looking for both deep knowledge and enthusiasm. Most likely the issue of getting funding or not depends on how much confidence he/she has in you rather then your past. But there will be competition, even there.

But if you don't ask, you don't get an answer.

Overall grades don't matter as much as your specific grades. Remember a PhD will be focused on quite a narrow field. If, for example, you're going into a dynamics PhD, and you have first class marks in dynamics, a dynamics based dissertation, and rubbish statistics grades that pull down your overall, then it probably wouldn't matter too much. Research is different to exams. It's not as much of a memory test and requires different skills, more creativity and perseverance than ability to recall past papers, and selection panels understand that.

If you're looking at something in applied maths, then how much you know about the application will play heavily into it too. My PhD was mathematical modelling in cardiology, and going into the interview having read quite a bit about the various existing approaches probably went a long way to helping me, with average grades from an average uni, get a PhD position at a top 10 university in the UK. When I applied for my PhD I was told in the interview 'I see your Groups Theory mark was quite low, I hated that subject too', and was given the position because I 'clearly had the right ethos for the project' after complaining about how most of the research in the field doesn't make their application clear enough.