U.S. Customs and Border Patrol Cmdr. Gregory Bovino was set to face tough questions in a deposition Thursday, in part of an ongoing fight over how federal agents are handling immigration enforcement in Chicago.

At 10 a.m. Thursday, Bovino began testifying for a deposition that is expected to last about five hours. He will be questioned about how his agents carried out arrests that turned chaotic earlier this month.

Court filings show Bovino and two other federal officials — Russell Hott and Daniel Parra — will sit for depositions that will be recorded on video. Hott, the field director for Immigrations and Customs Enforcement in Chicago, sat for a deposition in Washington, D.C., on Wednesday. Parra, deputy chief patrol agent a Customs and Border Protection, will sit for a deposition on Friday.

Attorneys for protesters and press say federal agents fired chemical agents and used crowd control devices during immigration operations in Chicago's Little Village neighborhood and west suburban Cicero.

They also accuse the U.S. Department of Homeland Security of posting edited body camera and drone video online while refusing to turn over unedited versions.

This comes after a federal appeals court eased some restrictions against Bovino. On Wednesday, a federal appeals court granted a request from the U.S. Department of Justice for an administrative stay pausing an order that requires Bovino to meet in person with U.S. District Judge Sara Ellis each day.

Judge Ellis ordered the meetings after a hearing on Tuesday in federal court over alleged violations by Bovino and other federal agents of her temporary restraining order largely prohibiting the use of tear gas and other riot control measures on journalists, protesters and clergy during Operation Midway Blitz in Chicago.

In response to numerous filings regarding violations of that order, Ellis instructed Bovino to meet with her every weekday evening to go over the events of the day until a preliminary injunction hearing on Nov. 5.

In their filing to the U.S. Court of Appeals for the Seventh Circuit, lawyers for the government argue the order "far exceeds the recognized bounds of discovery" and "significantly interferes" with Bovino's function, which the government argues is "ensuring the Nation's immigration laws are properly enforced."

They also argue the meetings are "untethered to the plaintiffs' underlying claims" and go beyond reasonable necessity to comply with the court orders already in place.

On Wednesday afternoon, the court granted the administrative stay. So while Bovino may not have to appear before Judge Ellis now, he still has to hand over body camera video and arrest records by Friday.

Judge Ellis on Wednesday ordered Bovino to inform her of everyone who has been arrested during Operation Midway Blitz for non-immigration-related reasons, starting on Sept. 2 when Operation Midway Blitz began and continuing into the future. 

"In the grand scheme of things, a very minor victory for the government," said CBS News Chicago Legal Analyst Miller. "A short-term win, but the merits of the case will yet to be decided."

Bovino and one other official appeared in person for the deposition Thursday, and the third official was to appear virtually from Washington, D.C.