I got a paper to review from a journal that had rejected my earlier works, how to respond?

These two issues are separate: if they reject your paper without comments, that's where you have to complain. They did not do a good job, reputable or not, and you are entitled to an explanatory review, especially since they wasted your time.

But you should not link the issues. If you think the journal is not as good as it used to be, you can decide not to review. If you think it is good, then, depending on how much time you have, you can offer to do the review. And if you do, do it with as much goodwill as you would for a journal that gave your astounding reviews.

But you should not link your rejection and your review - it is tempting to do so, but it is not a professional attitude. And you want to be just that: a professional.

Is it weird that the journal is now thinking me capable of reviewing a manuscript?

Not really. Almost all scientists have their papers rejected on a regular basis and if this disqualified them from reviewing, journals would be running out of reviewers extremely quickly. Moreover, highly ranking journals reject papers mainly for their lack of importance, not for being technically bad. So, assuming that you have some publications elsewhere to advertise your qualities and your paper was not rejected for outrageous problems (such as plagiarism), I do not find this weird.

Should I accept the review invitation? Or, should I just say that I can't do the review, which will be like Tit-For-Tat.

Only you can make this decision, but consider these points:

• Seeking revenge on a journal because they rejected your paper is neither ethical nor professional.

• On the other hand, if you think that the journal or publisher are generally practicing bad behaviour, you can refuse to review on that basis and should state your reasons. It is even okay if you make that judgment on basis of your own experiences – there is a crucial difference between “I refuse because you rejected my paper” and “I refuse because of how you rejected a paper (which happened to be mine)”. However, I think that if you do, you should have complained about these issues when your paper was rejected – after all whatever you experienced could be bad luck or due to a single bad editor.

Is it weird that the journal is now thinking me capable of reviewing a manuscript?

No, it isn't. Rejecting your papers was a judgement about those specific papers, not about your personal abilities as a scientist. It doesn't indicate that the journal somehow thinks you, personally, aren't good enough for their journal, it just means those particular papers didn't make the cut.

If your experience with the journal has actually poisoned your relationship with it - in particular, if you wouldn't submit again for fear of the same thing happening - then that's probably a reason to decline (perhaps just politely responding that you don't have the time, which is always a valid response). Answering that question probably means deciding whether you think the journal really mishandled your papers, and in a systematic enough way that you don't trust them to handle others, or if they just happened to reject them, or just had a one-time mess-up by a single editor.