If I choose to put Reaver's Row's "may" triggered ability on the chain targeting Irelia Fervent, can I decline to move her back to base when the ability resolves but still get the +1 might choose trigger?

No. Under the Unleashed rules update, if you decide to put a "may" triggered ability on the chain, you can no longer decline its effects when the ability resolves. If you choose to put Reaver's Row's ability on the chain targeting Irelia Fervent, you must move her back to base when it resolves. The "may" only gives you the option of whether to put the ability on the chain at all — once it's on the chain, the effect is mandatory. Note: Reaver's Row is banned in Standard Constructed as of March 31, 2026, but this ruling applies to similar "may" triggered battlefields like Amateur Recital, Star Spring, and Valley of Idols.