In the press of the time, the relationship between the Queen and Thatcher was always played as what could best be described as frosty, following an apparent narrative that Thatcher saw the Queen as a challenge to her national matriarchy. Thatcher famously used the royal 'we' to refer to herself when she became a grandmother: https://www.youtube.com/watch?v=s5Gxruh-pLI

However, this narrative is somewhat convenient and relatively unsupported by evidence. The PM has a weekly audience with the Queen, and the Queen has always historically avoided public discussion of these meetings, or her personal feelings about the various PMs, wisely remaining as disinterested as possible. Thatcher in her memoirs makes scant mention of the meetings.

There are some references to feelings being made on public occasions. From 'Political Issues in Britain Today' by Bill Jones:

Apparently the Queen spoke dismissively when the Prime Minister fainted at a Palace function: "She's keeled over again", she said to fellow guests.

There is also reference to them clashing over sanctions against apartheid South Africa (Thatcher in opposition [to sanctions], The Queen in support).

Anthony Sampson, a journalist of the era well-known for being well-ensconced within the corridors of British power, wrote in 1982: "The relationship is the more difficult because their roles seem confused. The Queen's style is more matter-of-fact and domestic while it is Mrs Thatcher (who is taller) who bears herself like a queen." He also refers to Thatcher being 'in urgent need of a drink' after her audiences.

But fundamentally the relationship between any PM and the Queen tends to be a secretive one, and particularly so in this case.

edit: I've also remembered that Thatcher's funeral was the first PM's funeral attended by the Queen since Churchill, but not too much should be read into this as hers was a state ceremonial funeral, and all the ones in between were private, so this should just be taken as The Queen obeying social norms.

edit2: also worth noting that The Queen conferred The Order of Merit on Thatcher 2 weeks after she resigned, which is within the personal gift of The Queen, as well as the other honours she gained subsequently