There's a misconception that every sentence using a quote structure has one and only one 'correct' form/transform/equivalent using a report structure. This theory certainly falls down for quote structures containing exclamatory utterances, for example
(see FumbleFinger's answer at Direct Speech to Indirect Speech).
Deictics within the quote also pose problems:
- "Is Jim here?" asked Jill. [locative 'here' cannot be retained in a report version]
- "What's that smell?" asked Bill. [locative 'that' cannot really be retained in a report version]
- "My back hurts" moaned Bob. [possessive 'my' cannot be retained in a report version]
- "We need it now!" she protested. [temporal 'now' cannot be retained in a report version]
- "We will need it tomorrow," he explained. [temporal 'tomorrow' cannot be retained in a report version]
Fixes here may (→ 'there'/ → ? / → 'his' / → 'then'/ → 'the next day') or may not be simple.
As a report usually looks back at an utterance, temporal deixis is very often problematic.
is readily converted to a report form, most commonly with backshifting:
- He said that he felt sick.
but also, if the statement is still relevant, alternatively with the present simple:
- He said that he feels sick [ ... that's why he's gone to see matron].
Sometimes, fixed expressions connected (perhaps loosely) to locatives / directionals / temporals are hard to 'convert':
- "What's this I hear about you and Cinderella?" asked Bill.
A complication involved in OP's example here is that the intro 'It's time that I / you / he/she/it / we / they' usually take a verb in the simple past.
As Rachel, a moderator at The Grammar Exchange explains (though the mention of 'conditional' here is probably unhelpful: 'counterfactual', yes):
"It's time (that)" and "it's about time (that)" introduce a kind of
conditional clause, a present contrary-to-fact situation. It's similar
to saying "I wish (that)" + the conditional. Past verb forms are used
to express a present time, although they may also refer to the future:
- It's time you cleaned this carpet, don't you think?
- It's time that we had a talk. I have something important to say.
- It's about time he found a wife and settled down. ...
So logically, one might expect
- The boss said, “It’s time we began planning our work.”
to use a backshift in a report equivalent.
But the only semi-relevant hit I've found for "time we had begun" (ie including it's) in a Google ngram search for time we began,time we had begun refers to its inclusion as a possible correct answer in the original of this question.
So it would seem that in practice the inflexibility of the expression 'It's time we + V-ed' overrides the tempting logical step of backshifting. This leaves
- The boss said that it was time they began planning their work.
as being probably the answer the examiners are after,
Though as @alphabet advises, a rewrite would be a better solution (but examiners tend to be at least as inflexible as fixed expressions).