Let's talk about 'tense' (that's how 'have' actually matters in your case). If you feel this TL;DR then jump to the bottom.
Tenses in English
The most ordinary and most basic tense is Simple Present. Like we often say,
There is a question on ELL SE and it is about tenses.
Simple & easy.
Basically advancing, there comes the Present Participle and it's probably the most commonly used tenst. Note that 'Participle' is often referred to as 'Progressive' or 'Continuous'.
I'm reading the question and I'm writing an answer.
(Not currently but recently doing) "What are you doing?" "I'm answering questions on SE."
For things happened in the past, we use Simple Past & Past Participle. They are simply the past tenses of the corresponding present tenses.
I said this is Simple Past. I was looking for good explanations.
For things that's going to happen in the future, we talk about them in future tenses, namely Simple Future and Future Participle.
I will give you a good answer. I will be sleeping at midnight.
There are also Past Future and Past Future Participle.
I knew you would understand this and I thought you would be reading my answer at 10 p.m.
There are perfect tenses for things already finished by a specific time. Perfect tenses can be combined with others. Like we say:
I have written more than 300 words so far and I've been writing this for half an hour.
I had reached 200 rep on ELL SE by midnight of yesterday.
This answer will have received 10 up votes by the end of this week.
(Occurrence time comparison) There had already been 2 answers when I saw this question.
(Subjunctive mood) If I had come earlier, I would have answered the first.
The ultimate complexity of tenses, the Past Future Perfect Participle. Just skim it over because you will hardly ever see this elsewhere except on ELL SE.
I would have been browsing Stack Overflow if I hadn't seen this question.
If you want to learn more, here's an article on Wikipedia. There's also a bunch of tutorials available through a simple Google query.
Now come back to your specific questions.
The study was about people who had struggled with alcoholism.
(Note "have" is incorrect here and I corrected it for you) There used to be a study. It was about people who had struggled with alcoholism before the study came out and were no longer struggling at the time of the study.
The study was about people who struggled with alcoholism.
There used to be a study. But this time it was about people who struggled before the study came out and were still struggling after the study had come out.
The participants have walked three miles.
I'm here and I'm saying now. The participants have already covered a distance of 3 mi by the time I'm speaking.
The participants walked three miles.
Yes they walked 3 mi but at present they are not walking anymore.
That's the difference. Without "have" it's Simple Past tense, while with "have" you're speaking in Present Perfect tense. "have" here is not redundant, it means a wholly different time tense.
P.S. If you don't want to Google around, I can tell you that "TL;DR" stands for "Too Long; Didn't Read". There's also an article on Wikipedia.
More P.S. I was about to add several links for every single concept when I suddenly realized that it was super duper easy to Google them all.