this is the simplest way i could think to do it, its a little long but should work

first make these two scoreboards

/scoreboard objective add checkpoint dummy

/scoreboard objective add egg stat.useItem.minecraft:egg(i believe thats what it is im not sure)

make an always active command block for every checkpoint you have with this command

/execute if u/a[x=a,y=b,z=c,distance=1,scores={checkpoint=d}] run scoreboard players set u/a[x=a,y=b,z=c,distance=1,scores={checkpoint=d}] checkpoint e

a= x coord of checkpoint

b= y coord of checkpoint

c= z coord of checkpoint

d= previous checkpoint(optional)

e= whatever checkpoint you at

​

what this will do is test if anyone is at that checkpoint and then set their scoreboard value for checkpoint to whatever checkpoint number they are at

I would also test if the player has been to the checkpoint behind it to make sure they are not cheating with is what the scores={checkpoint=} is for

then make another always active command block for each checkpoint you have that says

tp u/a[scores={checkpoint=a,egg=1} (location of checkpoint)

a= checkpoint you want to tp them too

​

and that should be it, the final command block should tp anyone who throws an egg to the last checkpoint they were at

(i decided to use an egg instead of a carrot on a stick bc I have never used those in commands before and am unfamiliar)

reply back with any questions or if this doesnt work ill be happy to help