It appears there is no strict threshold, but it depends on how many other assemblies for a given taxa are already submitted. I think their logic is it's okay to accept a lower quality genome if it's covering gaps in taxonomy until better ones come along.

In their prokaryotic release notes, this is what it says:

Added CheckM completeness cut-offs to validate annotation. An annotated assembly will only be added to the RefSeq collection if it meets the following criteria:
For species with more than 1000 assemblies in RefSeq, the completeness is higher than the species Average Completeness - 3 times the standard deviation . For species with 10-1000 assemblies in RefSeq, the completeness is higher than the smaller of 90% or the species Average Completeness - 3 times the standard deviation . No CheckM cutoff is applied if there are less than 10 assemblies in the species.

And with their documentation on selecting a genome, it appears CheckM is not considered for eukaryotic genomes.

RefSeq prokaryotic genomes are selected based on the criteria mentioned on this page: https://www.ncbi.nlm.nih.gov/refseq/about/prokaryotes/

For CheckM above page lists following criteria:

In order, assemblies with the highest quantized level of completeness (98 to 100) are preferred over assemblies in the 95-98, 90-95, 85-90, 70-85, 50-70, and under 50 percent level of completeness, as determined by CheckM.

RefSeq genome selection for eukaryotes is based on: https://www.ncbi.nlm.nih.gov/datasets/docs/v2/policies-annotation/genome-processing/refseq-selection/