Yes, Simple Past versus Present Perfect can be confusing. That said, one always has to remember to use an imaginary timeline where there is a line like this ____that extends forwards and backwards from a point, which is the present. The present for a speaker: _________________x_________________________
Quote With regard to: "last week", "last year", etc. we just can't use Perfect.
Lots of people ... (help) us last year and we want to thank everyone. Unquote
Let's look at the two ways to say it.
1) Lots of people helped us last year and we want to thank everyone.
Analysis: The speaker is speaking in the present and the year in question is finished. The speaker is speaking in 2017 and referring to 2016. So simple past.
2) Lots of people have helped us this past [or last] year and want to thank them.
Analysis: The speaker is speaking while the year is still in progress; it has not yet ended.
You can use PP with this week or this year, if the week or year is NOT YET ENDED when you say the sentence (time of speaking). This week [not yet over], I have thanked many people. This week, I thanked many people. [The TIME OF THANKING is over].
That said, in your example, the book is wrong: for PP to be possible, it has to be: Lots of people have helped us this year [where the year is not yet over].
It is not grammatical to say: Many people have helped us LAST YEAR because last year is always over. It's only with THIS YEAR that you can use either simple past (the action is over) or present perfect (the time period is not yet over).
Try to position yourself on the timeline at the x, speak the sentence and ask yourself: Is the time period over? Yes? Then, simple past (last year, last week) or Is the time period not yet over? EITHER simple past or simple perfect, depending on what YOU want to say re the action.
This week I have thanked many people [the week is not over and the action in the past is not specified as being at a specific moment]
This week I thanked many people. [the week is not over and I thanked them on Wednesday or Friday etc. The actual moment of thanking them that is over implies it was specifically at a time even IF they actual MOMENT is not mentioned.