In 1984 the Supreme Court, in a case called Chevron v. NRDC, established the principal that courts will defer to how a U.S. government agency interprets a U.S. rule or law. This is referred to as the Chevron doctrine.
The Supreme Court recently agreed to decide a new case, Loper Brights v. Raimondo, which challenges the Chevron doctrine and could potentially give courts more leeway in how to interpret ambiguous statutes.
Without Chevron, courts may be more free to protect the rights of immigrants by imposing their own interpretations of immigration laws.
I think, on balance, overturning Chevron would have a positive impact for immigration. Putting more authority in the hands of the judiciary should lessen the extreme policy swings that come with changes in presidential administrations.
It could also further balkanize how the law is applied depending on the circuit or district you live or sue in. Some districts are going to have draconian interpretations of laws and some more permissive. Most importantly, it could give more immigrants another, better bite at the apple, if an agency interpretation is hostile to their situation.
One result that is near certain if Chevron is overturned is that federal litigation will increase in frequency and become more consequential to immigration law.