US prosecutors said Pham was directed by al-Qaeda leader Anwar al-Awlaki to detonate explosives in Heathrow's arrivals area after spending several months in Yemen being trained by him.
In US court documents from 2015, Speitan was listed as a "close friend" of Pham who would provide "critical testimony regarding Pham's mental state".
The documents said that would be "crucial in establishing a mental health defense", adding that "bears on the issue of guilt".
Speitan had a medical condition that prevented her from giving evidence in person, the documents add.
In a later letter to the US District Judge, Speitan said Pham was one of the "few people I regard with such high respect and esteem".
She said if the judge "truly knew the Minh [Pham] that and others grew to love and respect", they may have "probably had the whole case dismissed".
She acknowledged he "may have had and developed some behavioural issues" but added: "He turned out to be one of the kindest, honest, most sincere, trustworthy and respectful people I have ever known."
There is no suggestion in the documents that Speitan knew of Pham's criminal activities at the time they knew each other.
Speitan has not responded to the BBC's request for comment. The Telegraph reported that when it asked her if she remained friends with Pham, she replied: "Yes, it's still the case."
She was reported as saying she believed Pham had been "targeted" by "the system".
A Green Party spokesperson said: "Where members have expressed views that do not fit in with the party's values, we have internal processes to investigate."
It came as Green leader Polanski grappled with division among the party's members, MPs and deputy leaders over the motion.
Some Green councillors have resigned since it was passed. Green deputy leader in Wales, Phil Davies, resigned and cancelled his membership on Tuesday, describing the motion as "the final nail in the coffin".
Polanski released a lengthy statement on Monday night to say he would not accept anyone being excluded from the party "because of the religious or communal body they are part of".
The party leader, who is Jewish, added that "antisemitism and criticism of the Israeli state are, and must always be, completely distinct".

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