802 Works Ltd claims the club has not paid a bill for work at Ibrox and wants the cash frozen to ensure payment if Rangers go bust.
Rangers say the firm breached the contract as the system cannot be used by 50,000 people at the same time.
A sheriff will rule on Friday whether an arrestment warrant granted two weeks ago should remain or be lifted.
At Glasgow Sheriff Court, lawyers for 802 Works said the firm wanted the money ring-fenced to ensure payment if the club goes into insolvency.
The court was told that Rangers "over a considerable period", had been operating at a loss of £7.5m per year.
Various accounts were lodged at the court, including an audited report dated October 2015, showing financial information and an account showing more recent figures that were taken from the club's account system.
The most recent figures were objected to by the representative of 802 Works.
Solicitor advocate Simon Catto, representing 802 Works, said the audited report showed a full year's accounts and a loss of around £7.5m per year should be preferred.
He said: "These are the only documents that should be looked at when considering if there is a risk of insolvency."
Counsel for the club, Christopher Wilson, told the court that the sum sued for is 2% of the turnover.
He said: "The company is turning over that amount each week."
The court heard Rangers have repaid a £5m loan from Sports Direct.
Mr Catto said the defence case, that only 10,000 users could access the Wi-Fi in the stadium and that constituted a breach of contract, was "feeble".
The court was told it was "quite clear from documents" that there was no intention that anything like 50,000 people would be able to use the system simultaneously.

Lee Cook's fourth-minute shot from the right-hand side of the penalty box was enough to separate the sides.
Brendan Moore denied Cook a second in the first half while Angus MacDonald twice went close for the Gulls.
Torquay, who had been on an eight-game unbeaten run, have now lost two in a row and are two points from safety.
They have scored just one goal in their last six games and dropped to third from bottom of the table after Boreham Wood's 3-0 win over Dover.
A company which provided Wi-Fi services to Rangers is bidding to have £300,000 of the club's cash ring-fenced.
[NEXT_CONCEPT]
Eastleigh moved to within two points of the National League play-off places as they won at relegation-threatened Torquay United.