What does Mardi Gras have to do with Easter?

Historically yes.

Mardi Gras means fat Tuesday

people gorge and party that day because the next day is Ash Wednesday - Lent - where people give up things

somehow I don't think God is pleased with that arrangement

Mardi Gras has nothing to do with easter

Fat Tuesday was originally a day when Catholic families would eat up their supply of butter and other rich food in preparation for the fasting in Lent (which begins the next day, Ash Wednesday). This simple celebration of eating really rich food evolved into all sorts of celebrations like Mardi Gras and Carnival in Brazil.

Yep. There's Fat Tuesday and Ash Wednesday, which is the beginning of Lent. From then on, every Friday is meatless, until Lent is over. You also give up something (cokes, ice cream, whatever) for the 40 days. Followed by the week before Easter, including Maundy Thursday (also called Holy Thursday), Good Friday, Holy Saturday, and Easter Sunday. His rising again, on Easter Sunday, is the end of the Lenten season.

Giving something up is the way we show that we stand with the Lord, because he wandered for 40 days, fasting and praying, and so we try to show devotion by giving something up.

Yes. Mardi Gras is a mixture of Creole Catholic celebration.

Mardi Gras is that the last day of celebration before the austerity of Lent. While not a Catholic holiday, it was traditional for the general populace to engage in this one day of celebration.

<<What does Mardi Gras have to do with Easter?>>

Nothing. It's more to do with the beginning of Lent, rather than Easter itself.

<<Every year Mardi <snip> then Ash Wednesday.>>

Yeah, like I said.

<<After Lent, Easter <snip> a Catholic holiday?>>

It's not necessarily "Catholic" since there is nothing theological about Mardi Gras itself.

It's just a tradition to have a carnival before the beginning of Lent. Since so many people give up things during lent, they had a big party just before lent. The party kept getting bigger over the ages.

Nothing, it is a cultural custom before Lent when most Catholics and some Protestant traditions fast or give up something. It is a time to indulge before the giving up of the item of pleasure.

It is from Catholics, but it is not a holiday on the church calendar. It is a folk holiday that arose from the practice of Catholicism.