The rapid advancement of generative artificial intelligence (GenAI), particularly tools like ChatGPT, has introduced both opportunities and challenges for academic assessment in higher education. This systematic review explores how GenAI has influenced academic integrity concerns and highlights the assessment redesign strategies proposed or implemented in response. Drawing from 18 peer-reviewed articles published between 2022 and 2025, the review identifies seven key thematic areas: integration of GenAI in educational settings, pedagogical opportunities, integrity-related challenges, impacts on critical thinking and originality, educator and student perspectives, practical implementation outcomes, and strategic recommendations. While GenAI offers personalized feedback, improved access, and scaffolding for learning, it also raises critical issues, including plagiarism, superficial engagement, and the erosion of authorship. The review further reveals a lack of institutional policy, inconsistent ethical guidelines, and disparities in GenAI access among students. In response, researchers advocate for AI-resilient assessment models, ethical literacy, and adaptive institutional frameworks. Although the reviewed studies are general, these issues are critical in mathematics education, where assessment emphasizes reasoning and problem-solving. GenAI may bypass key cognitive processes, undermining assessment validity. The findings suggest proactive, pedagogically informed assessment redesign that leverages GenAI while safeguarding academic integrity, particularly in mathematics learning contexts.