Before we answer the question, let us look up ITT Tech on Wikipedia. Let us look at the accredition information:
ITT Tech is nationally accredited by the Accrediting Council for Independent Colleges and Schools.
Now that you know that ITT Tech is nationally accredited, let's find out what it means to be nationally accredited in our context. Here's a quote from another Wikipedia article:
Every college has the right to set standards and refuse to accept transfer credits. However, if a student has gone to a nationally accredited school it may be particularly difficult to transfer credits (or even credit for a degree earned) if he or she then applies to a regionally accredited college, since some regionally accredited colleges have general policies against accepting any credits from nationally accredited schools, others are reluctant to because regional schools feel that national schools' academic standards are lower than their own or they are unfamiliar with the particular school.
So there you have it. It seems that the question is not about ITT Tech but nationally accredited vs regionally accredited higher education institutions in general. As I said earlier, I am not affiliated to ITT Tech in any way. Everything you read here could end up applying to you if you go to any other for-profit, nationally accredited vocational college.