BGP question

I have 2 routers running BGP, they are in the same AS, but not peered vis iBGP. They are both connected to the same eigrp network.

They are both connected via BGP to the same MPLS cloud. They redistribute the BGP routes into eigrp.

Here is my problem: they are learning about the internal routes via BGP, like router A will advertise 172.26.0.0/16 (an eigrp route) via BGP, and then router B will learn that route via BGP, and it is also learning about it via eigrp internally.

What do I need to do to stop this loop? I need my BGP routers to stop learning about each other's routes via BGP, but they both still need to advertise these routes to that MPLS network.