Israel already participates in the process. That's why they file documents with the court. Claims from two of those the pre-trial chamber rejected today, prior to issuing the warrants.

Re response: your claim was participation not jurisdiction, shift goalposts however you like

Sure, and in American courts you can appear just for the purposes of disputing jurisdiction without submitting oneself to it.

Disputing jurisdiction is submitting oneself to the court, so that the court may decide the issue of jurisdiction. If you submit such a jurisdictional dispute to the court for judgement, you tacitly agree to abide by the court's judgement in the dispute.

Here, the court made such a decision, Israel is just upset they didn't prevail. If Israel didn't think the court was allowed to rule on jurisdiction, Israel would not have submitted a petition for the court to do exactly that.