Gemma Wilkinson, a former charity worker, took legal action in an attempt to force Anjum to reveal the whereabouts of her daughter Atiya.
Anjum, who represented himself at the latest court hearing, indicated that Atiya was in Pakistan or Iran but said he did not know her exact whereabouts.
Mr Justice Moor said he was sure Anjum was lying.
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A woman hit by police gunfire during a counter-terrorism operation has been arrested after being released from hospital.
Police have been granted extra time to question a man who is being held on suspicion of planning a terror attack.
The man opened fire at the house, shattering the front door and window.