It is difficult to generalize the effect of biased study on the evaluation of a specific outcome but generally this leads to higher effect than the true effect. For example you would find a higher effect in a paper which bias is a specific case selection leading to a population where your intervention under investigation is working better. To my knowledge there is no written rule to decide when to exclude a biased study. The risk of bias (ROB) tools helps in determining where is the type of bias and its nature. If the overall quality of the paper is good enough to be included in the meta-analysis you can still look at the impact of this study in sensitivity analysis of the model or accounting on the overall study quality in meta-regression.
In this case, there are too few studies and they are too homogeneous in terms of risk of bias for a meta-regression or subgroup meta-analysis to make sense. If it is a subjective outcome measure the review is concerning, then the lack of blinding might have a large impact on the effect estimates. If it is a more objective outcome, such as a blood sample, then the lack of blinding might not be important.
An example of a risk of bias subgroup analysis an the interpretation can be found in the supplementary material of this article: Article Efficacy of low-level laser therapy on pain and disability i...