Conducting a literature review following an established strategy enables the analysis of the most recent studies that have been included. Consider excluding those predatory journals/publishers if they have poor quality ratings. Of course, they can also be directly set as the criteria for excluding documents. Sensitivity analyses can also be performed to see if the results of these studies are statistically significant for pooled effects before considering exclusion. Of course, these processes should be discussed in additional detail.

I think the type of journal should not a priori be an exclusion factor. You can have poor quality studies published in high impact journals (it always depends on the reviewers' that were selected to assess paper during the peer-reviewed process). Quantification of the studies' quality and risk of bias would be more robust than a priori excluding an eligible study just because it was published in a journal that is thought to be predatory.

My 2 cents.

NB: the definition of what is a predatory journal is still a debated issue.

I have come across eligible studies in predatory journals in two of my systematic reviews. Firstly, I contacted the corresponding author, to see if the study was real, and if it was published elsewhere or contained in a thesis. If there was no reply, which there was usually not, I excluded the study.

One of these studies had clearly fake data, so I would not include them in a review, without confirmation from the corresponding author that this was actually a real study, published by mistake in a predatory journal. Even then, I would probably only include it if the corresponding author could supply a related publication in a non-predatory journal.

'No data is better than bad data', don't ruin your review by including fake studies.