Do Tier-1 grad schools have a GPA filter
In my experience, no. The only automatic filter is for the university's minimum required TOEFL score; this requirement is imposed by the university and is not under the department's control.

Furthermore, for international students coming from academic systems that the committee is less familiar with, the GPA is less informative. If you weren't familiar with the Italian system, for example, it would be hard to know what a grade of 27 represents. So in these cases the admissions committee is likely to rely even more on the letters of recommendation. For a successful application at a "Tier-1 school", the letters likely need to come from someone knowledgeable about the reality of such a program (perhaps they received their PhD from a comparable department, or taught there in the past) and make a convincing case that you could be successful there. Even an extremely strong letter saying "This is the strongest student in Country X this year" might not be sufficient, if the committee doesn't have sufficient information to compare that with other applicants.

Source: I have served on grad admissions at a Tier-1 math department.