Is there a way to enter an order which seeks price improvement?

SMART is IBKR's "SmartRouting" algorithm which searches for the best stock, option, and combination prices available at the time of your order, and seeks to immediately execute your marketable order electronically at the best available price. 

Find out more about configuring for SmartRouting in the TWS Users' Guide…

We support the following routing destinations for IBKR Order Management System (IBKR OMS):

• IB SmartRouting^SM - Send electronic orders to the IB SmartRouting engine, which searches for the best price across different market centers trading the same product and seeks to execute your order at the best possible price…

Interactive Brokers uses its SmartRouting system to determine the best execution venue(s) for each order. For some products, IBKR customers may directly route their orders to a particular market of their choice. IBKR also operates an Alternative Trading System (ATS) in accordance with SEC Regulation ATS, on which it executes IBKR customer trades against each other or against one or more professional liquidity providers who send orders into the IBKR ATS. Order executions on IBKR’s ATS eliminate exchange fees and may offer price improvement compared to the NBBO. …

In TWS Global Configuration, the Smart Routing settings page provides checkboxes that allow you to either:

• Allow Smart routing to search for hidden liquidity at a better price than the NBBO in dark pools for stock/warrant orders ("Seek Price Improvement" checkbox)…