constant contact anti spam policy

Hi everyone. I wanted to know if anyone has experience with importing a decent sized email list to Constant Contact. I have a few clients who have given me their contacts some are 1000-3000 from emails or business cards over the years. I tried doing this sometime last year and Constant Contact. put a hold on my client's account and we had to ultimately remove the emails. When they asked this question which is basically, do your users on the email list consent to you having to email them? I wanted to be truthful so I picked NO at the time and I guess it prompted the hold on the account. I want to avoid this and lying to constant contact.

I'm sure if I added maybe like 50-100 per few days it might work but I was wondering if there was another solution or maybe just another platform I can use to email a large list. Any help or input is appreciated!