Please do not confuse Trade Marks, Domain Names and Copyrights. It appears that 'Complaints.com' is a registered trade mark in United States apart from, as you would appreciate, a registered domain name as well. Trade marks are territorial but because of accessibility of internet from any part of the world, domain names cannot be called territorial however the work carried out by a website may be territorial.
Moreover, trade mark disputes are resolved by courts in that jurisdiction in which the trade mark is registered and has been infringed. Domain name disputes may be resolved throught Courts (as has been done in many instances in India now) or there is a separate resolution fora called Uniform Domain Name Dispute Resolution Policy (UDRP) administrated by ICANN.
In the present scenario, complaints.com appears to be a US specific website while yours, I assume, would be an India specific website. I do not know what work you would be carrying out on your website but it is unlikely that a domain name dispute would arise in this case.
Further, 'complaints.com' is a trade mark in US and as you have pointed out, TM are territorial and therefore it cannot be enforced in India unless it has been registered as a TM in India as well. One exception is for well known trade marks which does not apply here.
Hope this helps.
B.R.Bhalla & Associates