If "can" can't be used in the past, so why the rule in the book named "New Round Up 5 students book" says the following: can't/couldn't + perfect infinitive = it's impossible that something happened in the past. Example: She can't/couldn't lost her way (=it's not possible she lost he way.). So, according to the rule "can't" can be used with past participle. I am confused. pleas help
Formally, most modals have a present and a past form, e.g. Can/could, will/would, shall/should, may/might.
I have no idea what you mean by a perfect infinitive.
"She can't have lost it" means it was not possible for her to lose it at any time in the past up to the present.
"She couldn't have lost it" means exactly the same thing.
Why does the tense of the modal not make any difference?
Because "lost" conveys the timing of the event on its own. So the tense of the modal is irrelevant.
Personally, I think it is better style to make the tense of the modal and main verb agree in this case, but millions have a different opinion.