The scientists modified the genes that were turned on/off (expressed) in mice. What happened to the offspring of these mice?

The resulting mice will be induced with the changed gene either on or off. The offspring will have altered genes if both the alleles have the trait. This is a heritable change.

Explanation:

Making gene on or off is a process of gene regulation when one of the gene is methylated or histone modification to prevent access to transcription factors hence no expression of the protein. This process is called epigenetics.

The resulting progeny in mice will receive the allele of on or off the gene. Such genes with altered allele are also called as

The altered genes will be expressed in the resulting progeny of mice.

The epigenetic genes can be reverted with environmental effects in the offspring paramutable alleles. They are heritable.