Mr Grieve indicated that the final text of the amendment tabled in the House of Lords at the last possible moment on Thursday had been changed from the wording which he believed had been agreed earlier in the day.
The disagreement centers on whether the government agreed to consider a specific clause of the rebel proposal that would hand parliament control of the Brexit process if ministers are unable to strike an exit deal by February 15, 2019.
Signalling rebels will seek to remove the unamendable nature of the government's proposal, she tweeted: "Would be amusing if only it wasn't such a serious issue, preventing the most destructive Brexit matters to the majority in parliament".
The upper House of Lords, which wants to keep Britain close to the European Union after the United Kingdom leaves in March, will rake over the EU (Withdrawal) Bill on Monday (Jun 18), before it returns to the lower House of Commons on Wednesday. However, they have fallen into a row with pro-EU Conservative lawmakers who want parliament to have a say in the exit process if talks in Brussels fail to reach an acceptable divorce deal.
Instead, MPs would be allowed to vote only on a "neutral" motion, confirming that they have considered a statement by a minister on the issue. I listened to their concerns and I undertook to consider their concerns.
The government could yet suffer a damaging rebellion on key Brexit legislation after Tory rebels were left unhappy at ministers' "sneaky" efforts at a compromise. The spokeswoman said the government had listened to MPs who had called for the "ability to express their views, in the unlikely event that our preferred scenario did not come to pass".More news: Trump says we'll 'know soon' if deal with North Korea will happen
That was the frank message from Tory MP Mike Wood, who has warned his fellow politicians that people are sick and exhausted of them bickering amongst themselves over the UK's departure from the EU.
Mr Wood said MPs had wasted too much time "negotiating with ourselves and arguing ourselves down", which he said "we should be beyond by this point".
She said that in the week beginning Jul 9 the government would set out in more detail than ever before its ambition for future relations with the EU.
"It all changed without Dominic Grieve or anyone else being consulted".
The latest internal dispute concerns the role of the UK Parliament in the event that the government's negotiations with Brussels produce no agreement, shortly before the country is due to leave the European Union in March next year. Ministers are digging in and refusing to give ground for now.
Shadow Brexit secretary Sir Keir Starmer said: "The Government's amendment is simply not good enough".
"Similarly we must have an independent trade policy, and that does not mean staying in the customs union with the EU".
"The meaningful vote is going to be either the government's deal is accepted in which case that is the meaningful vote to accept it or it isn't accepted, in which case frankly there is going to be a new government", he told "Sky News".