Not peremptory strikes, but you have unlimited removals for cause (and admittedly a steep appellate hill to climb if they’re unfairly denied)
The judge might allow it, but the odds are long and the next judge will certainly allow an appeal on those grounds so you probably don't even gain much except time.
If you do something slimy like dismiss a huge fraction of the juror pool because you don't like their demographics (vs for example having to dismiss the half of the population that had their opinion biased by the news or some other non-slimy reason to cause the same outcome) there will be an appeal and that appeal will be presided over by a judge.