The purpose of cross-fostering the pups in the study by meaney (so that mothers of high maternal care fostered pups of low maternal care mothers and vice versa) was

To control for mother's genetic contribution to the pup's temperament (e.g fearfulness or anxiety).

Explanation:

Cross-fostering is a method used for the purpose of animal husbandry, veterinary science, genetic, nature versus nurture studies, and conservation studies. In this approach the offspring are separated from their birth givers or parents after birth and raised by surrogates.  

The offspring may show their response by identifying that the surrogates are not their original parents by temperament and anxiety which is because of the genetic contribution of the mother in them.