Cardinality estimation is a key bottleneck for cost-based query optimization, yet deployable improvements remain difficult: classical estimators miss correlations, while learned estimators often require workload-specific training pipelines and invasive integration into the optimizer. This paper presents TiCard, a low intrusion, correction-based framework that augments (rather than replaces) a database's native estimator. TiCard learns multiplicative residual corrections using EXPLAIN-only features, and uses EXPLAIN ANALYZE only for offline labels. We study two practical instantiations: (i) a Gradient Boosting Regressor for sub-millisecond inference, and (ii) TabPFN, an in-context tabular foundation model that adapts by refreshing a small reference set without gradient retraining. On TiDB with TPCH and the Join Order Benchmark, in a low-trace setting (263 executions total; 157 used for learning), TiCard improves operator-level tail accuracy substantially: P90 Q-error drops from 312.85 (native) to 13.69 (TiCard-GBR), and P99 drops from 37,974.37 to 3,416.50 (TiCard-TabPFN), while a join-only policy preserves near-perfect median behavior. We position TiCard as an AI4DB building block focused on deployability: explicit scope, conservative integration policies, and an integration roadmap from offline correction to in-optimizer use.